{"id":496356,"date":"2026-09-28T10:08:04","date_gmt":"2026-09-28T10:08:04","guid":{"rendered":"https:\/\/savepearlharbor.com\/?p=496356"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=496356","title":{"rendered":"Flow Matching: \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0438 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f"},"content":{"rendered":"<div xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\">\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/2e4\/d0e\/d67\/2e4d0ed67be92dcce5f6a9ce54b79b1e.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 1. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0435\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439: \u0438\u0437 \u0448\u0443\u043c\u0430 \u043f\u043e\u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0432\u0438\u0434\u0435\u043e, \u0437\u0432\u0443\u043a \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0435 \u043e\u0431\u044a\u0435\u043a\u0442\u044b\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/2e4\/d0e\/d67\/2e4d0ed67be92dcce5f6a9ce54b79b1e.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/2e4\/d0e\/d67\/2e4d0ed67be92dcce5f6a9ce54b79b1e.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 1. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0435\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439: \u0438\u0437 \u0448\u0443\u043c\u0430 \u043f\u043e\u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0432\u0438\u0434\u0435\u043e, \u0437\u0432\u0443\u043a \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0435 \u043e\u0431\u044a\u0435\u043a\u0442\u044b<\/figcaption><\/div>\n<\/figure>\n<p><strong>Flow Matching<\/strong> \u2014 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0439 \u043f\u043e\u0434\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f. \u041e\u0441\u043d\u043e\u0432\u043d\u0430\u044f \u0438\u0434\u0435\u044f \u2014 \u043d\u0430\u0443\u0447\u0438\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u043e\u0441\u0442\u0435\u043f\u0435\u043d\u043d\u043e \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u0448\u0443\u043c, \u0432 \u0441\u043b\u043e\u0436\u043d\u044b\u0435 \u0434\u0430\u043d\u043d\u044b\u0435 \u2014 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0432\u0438\u0434\u0435\u043e, \u0437\u0432\u0443\u043a, 3D-\u0441\u0446\u0435\u043d\u044b \u0438\u043b\u0438 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u0440\u043e\u0431\u043e\u0442\u0430.<\/p>\n<p>\u0412 \u0440\u0430\u043c\u043a\u0430\u0445 \u0441\u0442\u0430\u0442\u044c\u0438 \u0440\u0430\u0437\u0431\u0435\u0440\u0451\u043c \u0443\u0441\u0442\u0440\u043e\u0439\u0441\u0442\u0432\u043e Flow Matching\u2019\u0430: \u043a\u0430\u043a \u0437\u0430\u0434\u0430\u0451\u0442\u0441\u044f \u043f\u0443\u0442\u044c \u043e\u0442 \u0448\u0443\u043c\u0430 \u043a \u0434\u0430\u043d\u043d\u044b\u043c, \u0447\u0435\u043c\u0443 \u0443\u0447\u0438\u0442\u0441\u044f \u043c\u043e\u0434\u0435\u043b\u044c \u0438 \u043a\u0430\u043a \u043f\u043e\u0441\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0438\u0437 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0433\u043e \u0448\u0443\u043c\u0430 \u043f\u043e\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u043e\u0432\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442. \u041e\u0431\u0441\u0443\u0434\u0438\u043c \u0433\u043b\u0430\u0432\u043d\u044b\u0439 \u043d\u0435\u0434\u043e\u0441\u0442\u0430\u0442\u043e\u043a \u043f\u043e\u0434\u0445\u043e\u0434\u0430 \u2014 \u043c\u0435\u0434\u043b\u0435\u043d\u043d\u0430\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044f (\u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043e\u0434\u0438\u043d \u043e\u0431\u044a\u0435\u043a\u0442, \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u043c\u043d\u043e\u0433\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0448\u0430\u0433\u043e\u0432).<\/p>\n<p>\u041e\u0434\u0438\u043d \u0438\u0437 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0435\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u2014 <strong>\u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f<\/strong>. \u041c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043c \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u043e\u043c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0437\u0430 \u043e\u0434\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0451\u0442 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u044b\u0435 \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0438.<\/p>\n<p>\u041e\u0434\u043d\u0430\u043a\u043e \u0442\u0430\u043a\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c \u043d\u0435\u043b\u044c\u0437\u044f \u043f\u0440\u043e\u0441\u0442\u043e \u043e\u0431\u0443\u0447\u0438\u0442\u044c \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0435\u0439 \u043f\u043e \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0443: \u00ab\u0412\u043e\u0442 \u2014 \u0432\u0445\u043e\u0434, \u0432\u043e\u0442 \u2014 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u0439 \u043e\u0442\u0432\u0435\u0442\u00bb. \u041c\u044b \u0440\u0430\u0437\u0431\u0435\u0440\u0451\u043c, \u043f\u043e\u0447\u0435\u043c\u0443 \u044d\u0442\u043e \u0442\u0430\u043a \u0438 \u043a\u0430\u043a \u0438\u0437 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442\u00a0<strong>\u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u0430\u044f \u043f\u043e\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430<\/strong>: \u0434\u0432\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430\u0447\u0438\u043d\u0430\u044e\u0442 \u0438\u0433\u0440\u0430\u0442\u044c \u0434\u0440\u0443\u0433 \u0441 \u0434\u0440\u0443\u0433\u043e\u043c, \u0430 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u0438\u0433\u0440\u044b \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c!<\/p>\n<h3>\u0421\u0444\u0435\u0440\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f<\/h3>\n<p>Flow Matching \u0441\u0435\u0433\u043e\u0434\u043d\u044f \u2014 \u043e\u0434\u0438\u043d \u0438\u0437 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0445 \u043f\u043e\u0434\u0445\u043e\u0434\u043e\u0432 \u0432 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u044f\u0445, \u00ab\u0440\u0430\u0432\u043d\u044b\u0439\u00bb \u0434\u0438\u0444\u0444\u0443\u0437\u0438\u043e\u043d\u043d\u044b\u043c \u043c\u043e\u0434\u0435\u043b\u044f\u043c (<a href=\"https:\/\/diffusionflow.github.io\" rel=\"noopener nofollow\">\u0432 \u043a\u0430\u043a\u043e\u043c-\u0442\u043e \u0441\u043c\u044b\u0441\u043b\u0435<\/a> \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u044d\u0442\u043e \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435).<\/p>\n<p>\u0418\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u2014 <a href=\"https:\/\/huggingface.co\/spaces\/stabilityai\/stable-diffusion-3.5-large\" rel=\"noopener nofollow\"><strong>Stable Diffusion 3.5<\/strong><\/a>, <a href=\"https:\/\/huggingface.co\/spaces\/black-forest-labs\/FLUX.2-dev\" rel=\"noopener nofollow\"><strong>FLUX.2<\/strong><\/a> \u0438 <strong>Kandinsky<\/strong> \u043e\u0442 \u0421\u0431\u0435\u0440\u0430. \u042d\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u044b \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0442\u044c \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u043e\u0435 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u0432 \u043d\u043e\u0432\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u2014 \u043e\u0442 \u0440\u0435\u0430\u043b\u0438\u0441\u0442\u0438\u0447\u043d\u043e\u0439 \u0444\u043e\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0438 \u0434\u043e \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0430\u043d\u0442\u0430\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0446\u0435\u043d\u044b.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/30d\/97a\/f89\/30d97af892184fc2e7dd12bef51b48ef.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 2. \u041f\u0440\u0438\u043c\u0435\u0440 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0439 \u0432 Stable Diffusion 3.5\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/30d\/97a\/f89\/30d97af892184fc2e7dd12bef51b48ef.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/30d\/97a\/f89\/30d97af892184fc2e7dd12bef51b48ef.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 2. \u041f\u0440\u0438\u043c\u0435\u0440 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0439 \u0432 Stable Diffusion 3.5<\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 Flow Matching\u2019\u0430 \u043d\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0438\u0432\u0430\u0435\u0442\u0441\u044f. \u0421 \u0435\u0433\u043e \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u043e\u0436\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0438 \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0435 \u043e\u0431\u044a\u0435\u043a\u0442\u044b \u2014 \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440,\u00a0\u0432\u0438\u0434\u0435\u043e \u0432\u043c\u0435\u0441\u0442\u0435 \u0441\u043e \u0437\u0432\u0443\u043a\u043e\u043c. MiniMax H3 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u043e\u0435 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u0441\u0446\u0435\u043d\u044b \u0438 \u043f\u043e\u0441\u0442\u0435\u043f\u0435\u043d\u043d\u043e \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u0448\u0443\u043c \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u0432 \u043e\u0434\u043d\u0443 \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0443, \u0430 \u0432 \u0446\u0435\u043b\u0443\u044e \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u043a\u0430\u0434\u0440\u043e\u0432 \u0438 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0439 \u0435\u0439 \u0437\u0432\u0443\u043a.<\/p>\n<div class=\"tm-iframe_temp\" data-src=\"https:\/\/embedd.srv.habr.com\/iframe\/6aba3c774d49dc1f038053fd\" data-style=\"\" id=\"6aba3c774d49dc1f038053fd\" width=\"\" data-habr-games=\"\"><\/div>\n<p>\u041d\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 \u0438\u0434\u0443\u0442 \u0435\u0449\u0451 \u0434\u0430\u043b\u044c\u0448\u0435: \u0441\u0435\u0433\u043e\u0434\u043d\u044f \u043e\u043d\u0438 \u0443\u043c\u0435\u044e\u0442 \u0441\u043e\u0437\u0434\u0430\u0432\u0430\u0442\u044c \u0443\u0436\u0435 \u043d\u0435 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0438\u043b\u0438 \u0432\u0438\u0434\u0435\u043e, \u0430 \u0446\u0435\u043b\u044b\u0435\u00a0<strong>\u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u044b\u0435 \u043c\u0438\u0440\u044b<\/strong>, \u0441 \u043a\u043e\u0442\u043e\u0440\u044b\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c \u0432 \u0440\u0435\u0430\u043b\u044c\u043d\u043e\u043c \u0432\u0440\u0435\u043c\u0435\u043d\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <strong>\u0441\u0435\u043c\u0435\u0439\u0441\u0442\u0432\u043e<\/strong>\u00a0<strong>Genie<\/strong> \u043e\u0442 Google DeepMind\u00a0\u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0432\u0438\u0440\u0442\u0443\u0430\u043b\u044c\u043d\u043e\u0435 \u043e\u043a\u0440\u0443\u0436\u0435\u043d\u0438\u0435 \u0438\u0437 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0438\u043b\u0438 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u043e\u0433\u043e \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u044f, \u0430 \u0437\u0430\u0442\u0435\u043c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u044c \u0435\u0433\u043e, \u0443\u043f\u0440\u0430\u0432\u043b\u044f\u044f \u043f\u0435\u0440\u0441\u043e\u043d\u0430\u0436\u0435\u043c. \u041f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f, \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438\u0434\u0443\u043c\u0430\u0442\u044c \u0438\u0433\u0440\u0443 \u0438 \u043f\u043e\u0447\u0442\u0438 \u0441\u0440\u0430\u0437\u0443 \u043e\u043a\u0430\u0437\u0430\u0442\u044c\u0441\u044f \u0432\u043d\u0443\u0442\u0440\u0438 \u043d\u0435\u0451!<\/p>\n<div class=\"tm-iframe_temp\" data-src=\"https:\/\/embedd.srv.habr.com\/iframe\/6aba3c7794d2580d55d47c09\" data-style=\"\" id=\"6aba3c7794d2580d55d47c09\" width=\"\" data-habr-games=\"\"><\/div>\n<h3>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/h3>\n<p><a href=\"https:\/\/arxiv.org\/pdf\/2210.02747\" rel=\"noopener nofollow\">Flow Matching<\/a> \u2014 \u043e\u0434\u0438\u043d \u0438\u0437 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u043f\u043e\u0434\u0445\u043e\u0434\u043e\u0432 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0439, \u0432\u0438\u0434\u0435\u043e, \u0437\u0432\u0443\u043a\u0430. \u0415\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u043d\u0430\u044f \u0438\u0434\u0435\u044f \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u0445\u043e\u0436\u0430 \u043d\u0430 \u0438\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e\u0435 \u00ab\u0440\u0430\u0441\u0448\u0443\u043c\u043b\u0435\u043d\u0438\u0435\u00bb: \u043c\u044b \u043d\u0430\u0447\u0438\u043d\u0430\u0435\u043c \u0441\u043e \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0433\u043e \u0448\u0443\u043c\u0430 \u0438 \u043f\u043e\u0441\u0442\u0435\u043f\u0435\u043d\u043d\u043e \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0435\u043c \u0435\u0433\u043e \u0432 \u043e\u0441\u043c\u044b\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442 \u2014 \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0432 \u0447\u0451\u0442\u043a\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/454\/090\/2c9\/4540902c903d5ec1b8e218dfd0fa709a.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 6. \u0418\u043d\u0442\u0443\u0438\u0446\u0438\u044f \u00ab\u0440\u0430\u0441\u0448\u0443\u043c\u043b\u0435\u043d\u0438\u044f\u00bb: \u0448\u0443\u043c \u043f\u043e\u0441\u0442\u0435\u043f\u0435\u043d\u043d\u043e \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043e\u0441\u043c\u044b\u0441\u043b\u0435\u043d\u043d\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/454\/090\/2c9\/4540902c903d5ec1b8e218dfd0fa709a.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/454\/090\/2c9\/4540902c903d5ec1b8e218dfd0fa709a.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 6. \u0418\u043d\u0442\u0443\u0438\u0446\u0438\u044f \u00ab\u0440\u0430\u0441\u0448\u0443\u043c\u043b\u0435\u043d\u0438\u044f\u00bb: \u0448\u0443\u043c \u043f\u043e\u0441\u0442\u0435\u043f\u0435\u043d\u043d\u043e \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043e\u0441\u043c\u044b\u0441\u043b\u0435\u043d\u043d\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435<\/figcaption><\/div>\n<\/figure>\n<p>\u0424\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_\\text{data} \\sim p_{\\text{data}}\" alt=\"x_\\text{data} \\sim p_{\\text{data}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/12\/128\/1289846f4c9fdeca643d8bfcf4b95660.svg\" width=\"96\" height=\"18\" data-width=\"12.048\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 12.048ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/12\/128\/1289846f4c9fdeca643d8bfcf4b95660.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/12\/128\/1289846f4c9fdeca643d8bfcf4b95660.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u042d\u0442\u043e \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0438\u0437 \u0438\u043d\u0442\u0435\u0440\u043d\u0435\u0442\u0430. \u041c\u044b \u0445\u043e\u0442\u0438\u043c \u043d\u0430\u0443\u0447\u0438\u0442\u044c\u0441\u044f \u043f\u043e\u0440\u043e\u0436\u0434\u0430\u0442\u044c \u043d\u043e\u0432\u044b\u0435 \u043e\u0431\u044a\u0435\u043a\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u0445\u043e\u0436\u0438 \u043d\u0430 \u0434\u0430\u043d\u043d\u044b\u0435 \u0438\u0437 \u044d\u0442\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043d\u043e \u043d\u0435 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043f\u0440\u043e\u0441\u0442\u044b\u043c \u043a\u043e\u043f\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432. \u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u0432\u044b\u0443\u0447\u0438\u0442\u044c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043a\u0430\u0440\u0442\u0438\u043d\u043e\u043a \u043f\u043e \u043d\u0430\u0431\u043e\u0440\u0443 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438\u0437 \u043d\u0435\u0433\u043e.<\/p>\n<p>\u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u0438\u0437 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043b\u0435\u0433\u043a\u043e \u043d\u0430\u0447\u0438\u043d\u0430\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044e. \u041e\u0431\u044b\u0447\u043d\u043e \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0431\u0435\u0440\u0443\u0442 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435: <img decoding=\"async\" class=\"formula inline\" source=\"x_\\text{noise} \\sim \\mathcal{N}(0, I).\" alt=\"x_\\text{noise} \\sim \\mathcal{N}(0, I).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3d1\/3d1ec568dfdea4e99e319bd35e1bfecb.svg\" width=\"127\" height=\"19\" data-width=\"15.855\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 15.855ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3d1\/3d1ec568dfdea4e99e319bd35e1bfecb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3d1\/3d1ec568dfdea4e99e319bd35e1bfecb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0418\u0437 \u043d\u0435\u0433\u043e \u043b\u0435\u0433\u043a\u043e \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u043d\u043e \u043e\u0431\u044b\u0447\u043d\u043e \u0432\u044b\u0441\u0442\u0443\u043f\u0430\u0435\u0442 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u043c \u0448\u0443\u043c\u043e\u043c.<\/p>\n<p>\u041a\u0430\u043a \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043f\u0435\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u0448\u0443\u043c\u0430 \u043a \u0434\u0430\u043d\u043d\u044b\u043c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0433\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t \\in [0,1]\" alt=\"t \\in [0,1]\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/df\/dff\/dff6e05ec00b53d46e366975136d0d2e.svg\" width=\"65\" height=\"18\" data-width=\"8.109\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 8.109ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/df\/dff\/dff6e05ec00b53d46e366975136d0d2e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/df\/dff\/dff6e05ec00b53d46e366975136d0d2e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>? \u0412 \u043c\u043e\u043c\u0435\u043d\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"t=0\" alt=\"t=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u044b \u043d\u0430\u0445\u043e\u0434\u0438\u043c\u0441\u044f \u0432 \u0448\u0443\u043c\u0435: <img decoding=\"async\" class=\"formula inline\" source=\"x_0 = x_\\text{noise} \\sim \\mathcal{N}(0, I),\" alt=\"x_0 = x_\\text{noise} \\sim \\mathcal{N}(0, I),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd2\/bd23f22b0289ed77e8583bcf1566f443.svg\" width=\"169\" height=\"19\" data-width=\"21.154\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 21.154ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd2\/bd23f22b0289ed77e8583bcf1566f443.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd2\/bd23f22b0289ed77e8583bcf1566f443.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0430 \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"t=1\" alt=\"t=1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0445\u043e\u0442\u0438\u043c \u043e\u043a\u0430\u0437\u0430\u0442\u044c\u0441\u044f \u0432 \u0434\u0430\u043d\u043d\u044b\u0445: <img decoding=\"async\" class=\"formula inline\" source=\"x_1 = x_\\text{data} \\sim p_{\\text{data}}.\" alt=\"x_1 = x_\\text{data} \\sim p_{\\text{data}}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f07\/f07bae1665e5d288bb37e892537c2d77.svg\" width=\"144\" height=\"18\" data-width=\"17.976\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 17.976ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f07\/f07bae1665e5d288bb37e892537c2d77.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f07\/f07bae1665e5d288bb37e892537c2d77.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c, \u0447\u0442\u043e \u043a\u0430\u0436\u0434\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0434\u0432\u0438\u0436\u0435\u0442\u0441\u044f \u0432\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438: \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043e\u043d\u0430 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u043a\u0430\u043a \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u0448\u0443\u043c, \u0430 \u0437\u0430\u0442\u0435\u043c \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u043c \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435\u043c.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/f10\/146\/029\/f10146029d8553fc2481c91942d433f1.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 7. \u0421\u0445\u0435\u043c\u0430 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0441\u0435\u043c\u043f\u043b\u043e\u0432 \u0438\u0437 \u0448\u0443\u043c\u043e\u0432\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f p_0 \u043a \u0441\u0435\u043c\u043f\u043b\u0430\u043c \u0438\u0437 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0434\u0430\u043d\u043d\u044b\u0445 p_1; x_t \u2014 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u044f\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/f10\/146\/029\/f10146029d8553fc2481c91942d433f1.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/f10\/146\/029\/f10146029d8553fc2481c91942d433f1.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 7. \u0421\u0445\u0435\u043c\u0430 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0441\u0435\u043c\u043f\u043b\u043e\u0432 \u0438\u0437 \u0448\u0443\u043c\u043e\u0432\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f p_0 \u043a \u0441\u0435\u043c\u043f\u043b\u0430\u043c \u0438\u0437 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0434\u0430\u043d\u043d\u044b\u0445 p_1; x_t \u2014 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u044f<\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u0430 \u0440\u0438\u0441\u0443\u043d\u043a\u0435 \u0432\u044b\u0448\u0435 \u043c\u044b \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u043c \u0432 \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u043f\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u0438 \u2014 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430, \u043f\u043e \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u0438 \u2014 \u0432\u0440\u0435\u043c\u044f), \u043b\u0438\u0431\u043e \u0432 \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u0448\u0443\u043c \u2014 \u0441\u043b\u0435\u0432\u0430, \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0438 \u2014 \u0441\u043f\u0440\u0430\u0432\u0430, \u0438 \u043c\u044b \u0434\u0432\u0438\u0436\u0435\u043c\u0441\u044f \u0432 \u044d\u0442\u043e\u043c \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0432\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438).<\/p>\n<p>\u041d\u043e \u0434\u043b\u044f \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0438 \u0434\u0440\u0443\u0433\u0438\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0435\u0442\u043b\u0438:<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/4e3\/cc2\/436\/4e3cc243625a1f8e3edb38bdde5bff5e.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 8. \u0421\u0445\u0435\u043c\u0430 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0441\u0435\u043c\u043f\u043b\u043e\u0432 \u0438\u0437 \u0448\u0443\u043c\u043e\u0432\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f p_0 \u043a \u0441\u0435\u043c\u043f\u043b\u0430\u043c \u0438\u0437 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0434\u0430\u043d\u043d\u044b\u0445 p_1 \u0441 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u043f\u0435\u0442\u0435\u043b\u044c\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/4e3\/cc2\/436\/4e3cc243625a1f8e3edb38bdde5bff5e.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/4e3\/cc2\/436\/4e3cc243625a1f8e3edb38bdde5bff5e.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 8. \u0421\u0445\u0435\u043c\u0430 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0441\u0435\u043c\u043f\u043b\u043e\u0432 \u0438\u0437 \u0448\u0443\u043c\u043e\u0432\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f p_0 \u043a \u0441\u0435\u043c\u043f\u043b\u0430\u043c \u0438\u0437 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0434\u0430\u043d\u043d\u044b\u0445 p_1 \u0441 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u043f\u0435\u0442\u0435\u043b\u044c<\/figcaption><\/div>\n<\/figure>\n<p>\u0421\u0430\u043c\u044b\u0439 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0441\u043e\u0435\u0434\u0438\u043d\u0438\u0442\u044c \u0448\u0443\u043c <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u043e\u0431\u044a\u0435\u043a\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u2014 \u043f\u0440\u043e\u0432\u0435\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438 \u043f\u0440\u044f\u043c\u0443\u044e \u043b\u0438\u043d\u0438\u044e:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_t = (1-t)x_0 + t x_1, \\qquad t\\in[0,1].\" alt=\"x_t = (1-t)x_0 + t x_1, \\qquad t\\in[0,1].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/add\/add5f7cea50528b2bf5d22dedb312597.svg\" width=\"272\" height=\"18\" data-width=\"33.965\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 33.965ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/add\/add5f7cea50528b2bf5d22dedb312597.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/add\/add5f7cea50528b2bf5d22dedb312597.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0440\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t=0\" alt=\"t=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u044d\u0442\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0434\u0430\u0451\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"x_t=x_0\" alt=\"x_t=x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/716\/716a5eb294a526b7a15085c0920f9138.svg\" width=\"59\" height=\"14\" data-width=\"7.358\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 7.358ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/716\/716a5eb294a526b7a15085c0920f9138.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/716\/716a5eb294a526b7a15085c0920f9138.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u043e \u0435\u0441\u0442\u044c \u0448\u0443\u043c. \u041f\u0440\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t=1\" alt=\"t=1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u043d\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"x_t=x_1\" alt=\"x_t=x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9fa\/9fa7d4e0b4acc2f0a8fe27dba26110b3.svg\" width=\"59\" height=\"13\" data-width=\"7.358\" data-height=\"1.676\" data-vertical-align=\"-0.357\" style=\"width: 7.358ex; height: 1.676ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9fa\/9fa7d4e0b4acc2f0a8fe27dba26110b3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9fa\/9fa7d4e0b4acc2f0a8fe27dba26110b3.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u043e \u0435\u0441\u0442\u044c \u043e\u0431\u044a\u0435\u043a\u0442 \u0438\u0437 \u0434\u0430\u043d\u043d\u044b\u0445. \u0410 \u043f\u0440\u0438 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u043e\u0447\u043a\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0433\u0434\u0435-\u0442\u043e \u043c\u0435\u0436\u0434\u0443 \u0448\u0443\u043c\u043e\u043c \u0438 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435\u043c.<\/p>\n<p>\u0421\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0432\u0434\u043e\u043b\u044c \u0442\u0430\u043a\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430 \u0438 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d x_t}{dt} = x_1 - x_0.\" alt=\"\\frac{d x_t}{dt} = x_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3bea659eb96ca1f8ee38dacdcfefa223.svg\" width=\"122\" height=\"37\" data-width=\"15.207\" data-height=\"4.676\" data-vertical-align=\"-1.773\" style=\"width: 15.207ex; height: 4.676ex; vertical-align: -1.773ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3bea659eb96ca1f8ee38dacdcfefa223.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3bea659eb96ca1f8ee38dacdcfefa223.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e \u0435\u0441\u0442\u044c \u0437\u0434\u0435\u0441\u044c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f (\u0432\u0435\u043a\u0442\u043e\u0440 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438) \u2014 \u0432\u0435\u043a\u0442\u043e\u0440 \u043e\u0442 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0448\u0443\u043c\u0430 \u043a \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u043c\u0443 \u043e\u0431\u044a\u0435\u043a\u0442\u0443.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/992\/73f\/770\/99273f77034861c1bbec130a27b5665c.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 9. \u041f\u0440\u043e\u0441\u0442\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439: \u043a\u0430\u0436\u0434\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0438\u0434\u0451\u0442 \u043a \u0432\u044b\u0431\u0440\u0430\u043d\u043d\u043e\u043c\u0443 \u043e\u0431\u044a\u0435\u043a\u0442\u0443 \u043f\u043e \u043f\u0440\u044f\u043c\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438, \u0430 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432\u0434\u043e\u043b\u044c \u043d\u0435\u0451 \u0440\u0430\u0432\u043d\u0430 x_1-x_0\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/992\/73f\/770\/99273f77034861c1bbec130a27b5665c.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/992\/73f\/770\/99273f77034861c1bbec130a27b5665c.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 9. \u041f\u0440\u043e\u0441\u0442\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439: \u043a\u0430\u0436\u0434\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0438\u0434\u0451\u0442 \u043a \u0432\u044b\u0431\u0440\u0430\u043d\u043d\u043e\u043c\u0443 \u043e\u0431\u044a\u0435\u043a\u0442\u0443 \u043f\u043e \u043f\u0440\u044f\u043c\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438, \u0430 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432\u0434\u043e\u043b\u044c \u043d\u0435\u0451 \u0440\u0430\u0432\u043d\u0430 x_1-x_0<\/figcaption><\/div>\n<\/figure>\n<p>\u0422\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0442\u043e\u0447\u0435\u043a (\u0438\u043b\u0438 \u0447\u0430\u0441\u0442\u0438\u0446) \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u043d\u043e \u0440\u0430\u0437\u043d\u044b\u043c\u0438. \u0412\u043c\u0435\u0441\u0442\u043e \u043f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u043d\u0438\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043b\u0438 \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 (\u0447\u0442\u043e \u043a\u0430\u0436\u0435\u0442\u0441\u044f \u043e\u0447\u0435\u043d\u044c \u0441\u043b\u043e\u0436\u043d\u044b\u043c, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043d\u0443\u0436\u043d\u043e \u0441\u043e\u043f\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0442\u044c \u0442\u043e\u0447\u043a\u0438 \u0438\u0437 \u0448\u0443\u043c\u0430 \u0441 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0430\u043c\u0438) \u043f\u043e\u043f\u0440\u043e\u0431\u0443\u0435\u043c \u043e\u043f\u0438\u0441\u0430\u0442\u044c \u0441\u0430\u043c\u043e \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0443\u0434\u043e\u0431\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u043e\u043b\u0435.<\/p>\n<p>\u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u(x,t)\" alt=\"u(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30b\/30bfdcfbd9a4e20bba0148762f16c555.svg\" width=\"49\" height=\"18\" data-width=\"6.171\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.171ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30b\/30bfdcfbd9a4e20bba0148762f16c555.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30b\/30bfdcfbd9a4e20bba0148762f16c555.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0433\u043e\u0432\u043e\u0440\u0438\u0442 \u043d\u0430\u043c, \u043a\u0443\u0434\u0430 \u0438 \u0441 \u043a\u0430\u043a\u043e\u0439 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c\u044e \u043d\u0443\u0436\u043d\u043e \u0434\u0432\u0438\u0433\u0430\u0442\u044c\u0441\u044f \u0438\u0437 \u0442\u043e\u0447\u043a\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0435\u0441\u043b\u0438 \u0441\u0435\u0439\u0447\u0430\u0441 \u043c\u044b \u043d\u0430\u0445\u043e\u0434\u0438\u043c\u0441\u044f \u0432 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u043e \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u(x_t,t)\" alt=\"u(x_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a49\/a49e4e1722ef09eebd045391fd8153d9.svg\" width=\"55\" height=\"18\" data-width=\"6.936\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.936ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a49\/a49e4e1722ef09eebd045391fd8153d9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a49\/a49e4e1722ef09eebd045391fd8153d9.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0448\u0430\u0433\u0430.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/b09\/c20\/1ee\/b09c201eef00952f9ba33fdbab4ac39b.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 10. \u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 \u2014 \u043d\u0430\u0431\u043e\u0440 \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0445 \u0441\u0442\u0440\u0435\u043b\u043e\u043a: \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043e\u043d\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u0442, \u043a\u0443\u0434\u0430 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0448\u0430\u0433\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/b09\/c20\/1ee\/b09c201eef00952f9ba33fdbab4ac39b.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/b09\/c20\/1ee\/b09c201eef00952f9ba33fdbab4ac39b.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 10. \u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 \u2014 \u043d\u0430\u0431\u043e\u0440 \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0445 \u0441\u0442\u0440\u0435\u043b\u043e\u043a: \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043e\u043d\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u0442, \u043a\u0443\u0434\u0430 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0448\u0430\u0433<\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043a\u043e\u0440\u043e\u0447\u0435, \u0447\u0435\u043c \u043e\u043d\u0438 \u0435\u0441\u0442\u044c, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0443\u0434\u043e\u0431\u043d\u043e \u0431\u0440\u0430\u0442\u044c \u0434\u0430\u043b\u0451\u043a\u0438\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0412 \u0442\u0430\u043a\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_1 - x_0\" alt=\"x_1 - x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg\" width=\"59\" height=\"14\" data-width=\"7.329\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 7.329ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0431\u0443\u0434\u0435\u0442 \u0431\u043e\u043b\u044c\u0448\u0438\u043c \u0438 \u0441\u043b\u043e\u0436\u043d\u044b\u043c \u0434\u043b\u044f \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f. \u0422\u043e\u0433\u0434\u0430 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u00ab\u0434\u043e\u043c\u043d\u043e\u0436\u0430\u0442\u044c\u00bb \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043d\u0430 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"d \\tau\" alt=\"d \\tau\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c4f\/c4fc9be191ddccbdcdc2369987afc09d.svg\" width=\"19\" height=\"18\" data-width=\"2.346\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.346ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c4f\/c4fc9be191ddccbdcdc2369987afc09d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c4f\/c4fc9be191ddccbdcdc2369987afc09d.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0415\u0441\u043b\u0438 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u043d\u0435\u0431\u043e\u043b\u044c\u0448\u043e\u0439 \u0448\u0430\u0433 \u043f\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"dt\" alt=\"dt\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg\" width=\"16\" height=\"13\" data-width=\"1.993\" data-height=\"1.595\" data-vertical-align=\"-0.025\" style=\"width: 1.993ex; height: 1.595ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043d\u043e\u0432\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0442\u0430\u043a:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_{t+dt} = x_t + dt \\cdot u(x_t, t).\" alt=\"x_{t+dt} = x_t + dt \\cdot u(x_t, t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/46\/463\/463aea1f38ccbd3b23fae2ba77aff854.svg\" width=\"190\" height=\"18\" data-width=\"23.749\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 23.749ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/46\/463\/463aea1f38ccbd3b23fae2ba77aff854.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/46\/463\/463aea1f38ccbd3b23fae2ba77aff854.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u044b \u0431\u0435\u0440\u0451\u043c \u0442\u0435\u043a\u0443\u0449\u0443\u044e \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043f\u043e\u043b\u0435, \u0438 \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u043f\u0435\u0440\u0435\u0434\u0432\u0438\u0433\u0430\u0435\u043c\u0441\u044f \u0432 \u044d\u0442\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/c32\/f23\/0ef\/c32f230efc1ff37c0a4d0bbdae593d7d.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 11. \u0421\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 x_1 \u043e\u0442 x_0 \u0432 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u043f\u043e u(x_t, t)\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/c32\/f23\/0ef\/c32f230efc1ff37c0a4d0bbdae593d7d.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/c32\/f23\/0ef\/c32f230efc1ff37c0a4d0bbdae593d7d.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 11. \u0421\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 x_1 \u043e\u0442 x_0 \u0432 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u043f\u043e u(x_t, t)<\/figcaption><\/div>\n<\/figure>\n<p>\u0418\u0442\u0430\u043a, \u0437\u0430\u0434\u0430\u0447\u0443 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u043c\u043e\u0436\u043d\u043e \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0442\u0430\u043a: \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u0431\u0443\u0447\u0438\u0442\u044c \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_{\\theta}(x,t)\" alt=\"u_{\\theta}(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg\" width=\"57\" height=\"18\" data-width=\"7.109\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.109ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u043e\u043b\u0435. \u041f\u043e\u0441\u043b\u0435 \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u0437\u044f\u0442\u044c \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u0448\u0443\u043c <img decoding=\"async\" class=\"formula inline\" source=\"x_0 \\sim \\mathcal{N}(0,I)\" alt=\"x_0 \\sim \\mathcal{N}(0,I)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg\" width=\"100\" height=\"19\" data-width=\"12.552\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.552ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u043f\u043e\u0441\u0442\u0435\u043f\u0435\u043d\u043d\u043e \u0434\u0432\u0438\u0433\u0430\u0442\u044c \u0435\u0433\u043e \u043f\u043e \u044d\u0442\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u043c\u0443 \u043f\u043e\u043b\u044e \u043e\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"t=0\" alt=\"t=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e <img decoding=\"async\" class=\"formula inline\" source=\"t=1\" alt=\"t=1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0415\u0441\u043b\u0438 \u043f\u043e\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u043e \u0445\u043e\u0440\u043e\u0448\u043e, \u0442\u043e \u0432 \u043a\u043e\u043d\u0446\u0435 \u044d\u0442\u043e\u0433\u043e \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0440\u0435\u0430\u043b\u0438\u0441\u0442\u0438\u0447\u043d\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435.<\/p>\n<p>\u0412 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0434\u043b\u044f \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u043f\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442 <strong>\u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u044b\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong> (ordinary differential equations \u2013 ODE). \u041c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u0445\u043e\u0442\u0438\u043c \u043d\u0430\u0439\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0437\u043d\u0430\u044f <img decoding=\"async\" class=\"formula inline\" source=\"x_0 \\sim \\mathcal{N}(0,I)\" alt=\"x_0 \\sim \\mathcal{N}(0,I)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg\" width=\"100\" height=\"19\" data-width=\"12.552\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.552ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0437\u0430\u043a\u043e\u043d <img decoding=\"async\" class=\"formula inline\" source=\"\\frac{d x_t}{d t} = u(x_t, t)\" alt=\"\\frac{d x_t}{d t} = u(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/252\/252b2c8920a16fd368cea4ac79a73f6c.svg\" width=\"113\" height=\"37\" data-width=\"14.185\" data-height=\"4.676\" data-vertical-align=\"-1.773\" style=\"width: 14.185ex; height: 4.676ex; vertical-align: -1.773ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/252\/252b2c8920a16fd368cea4ac79a73f6c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/252\/252b2c8920a16fd368cea4ac79a73f6c.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0418\u043c\u0435\u0435\u043c \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u0438 \u0437\u0430\u043a\u043e\u043d \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438, \u0437\u043d\u0430\u0447\u0438\u0442, \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043a\u043e\u043d\u0435\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443, \u043f\u0440\u043e\u0441\u0442\u043e \u043f\u0440\u043e\u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u0432 <img decoding=\"async\" class=\"formula inline\" source=\"x_s = x_0 + \\int_{0}^s u(x_t, t) dt\" alt=\"x_s = x_0 + \\int_{0}^s u(x_t, t) dt\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3f\/3fa\/3fa732061a49a2ef086f60eac0e8c0df.svg\" width=\"183\" height=\"42\" data-width=\"22.834\" data-height=\"5.232\" data-vertical-align=\"-2.05\" style=\"width: 22.834ex; height: 5.232ex; vertical-align: -2.05ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3f\/3fa\/3fa732061a49a2ef086f60eac0e8c0df.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3f\/3fa\/3fa732061a49a2ef086f60eac0e8c0df.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1 = x_0 + \\int_{0}^1 u(x_t, t) dt\" alt=\"x_1 = x_0 + \\int_{0}^1 u(x_t, t) dt\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae0\/ae02898796c65611bbf6d3da0bfe3b2a.svg\" width=\"183\" height=\"45\" data-width=\"22.934\" data-height=\"5.59\" data-vertical-align=\"-2.23\" style=\"width: 22.934ex; height: 5.59ex; vertical-align: -2.23ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae0\/ae02898796c65611bbf6d3da0bfe3b2a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae0\/ae02898796c65611bbf6d3da0bfe3b2a.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0433\u0434\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0437\u0432\u0435\u0441\u0442\u0435\u043d. \u042d\u0442\u043e \u043c\u044b \u0438 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u0443\u0435\u043c \u0447\u0435\u0440\u0435\u0437 \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0435 \u0448\u0430\u0433\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"dt\" alt=\"dt\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg\" width=\"16\" height=\"13\" data-width=\"1.993\" data-height=\"1.595\" data-vertical-align=\"-0.025\" style=\"width: 1.993ex; height: 1.595ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0415\u0441\u043b\u0438 \u043c\u044b \u0434\u043b\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043a\u0430\u0436\u0434\u044b\u0439 \u0440\u0430\u0437 \u0431\u0443\u0434\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u(x_t, t)\" alt=\"u(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg\" width=\"55\" height=\"18\" data-width=\"6.936\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.936ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043c\u044b \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0443\u0442\u0441\u044f \u0438 \u043e\u0442\u043e\u0439\u0434\u0443\u0442 \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430. \u0414\u0435\u043b\u043e \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u043f\u0440\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u0438 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0438 \u0434\u0430\u043b\u0435\u0435 \u043e\u0431\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043f\u043e\u0439\u0434\u0443\u0442 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"u(x_t, t)\" alt=\"u(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg\" width=\"55\" height=\"18\" data-width=\"6.936\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.936ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u043e \u0435\u0441\u0442\u044c \u0443\u0436\u0435 \u043d\u0435 \u0440\u0430\u0437\u044a\u0435\u0434\u0438\u043d\u044f\u0442\u0441\u044f.<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u0438\u0437\u0431\u0430\u0432\u0438\u043b\u0438\u0441\u044c \u043e\u0442 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0442\u044c, \u043a\u0430\u043a\u0438\u0435 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0442 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f\u043c. \u0414\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0437\u043d\u0430\u0442\u044c \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435.<\/p>\n<h3>\u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435<\/h3>\n<p>\u0412\u0435\u0440\u043d\u0451\u043c\u0441\u044f \u043a \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u0441 \u043f\u0440\u044f\u043c\u044b\u043c\u0438 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f\u043c\u0438. \u0412\u043e\u0437\u044c\u043c\u0451\u043c \u043f\u0430\u0440\u0443 \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432 <img decoding=\"async\" class=\"formula inline\" source=\"x_0, x_1\" alt=\"x_0, x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/057\/0578eb4988c85891fd365ff71c1e66d5.svg\" width=\"45\" height=\"12\" data-width=\"5.57\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 5.57ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/057\/0578eb4988c85891fd365ff71c1e66d5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/057\/0578eb4988c85891fd365ff71c1e66d5.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0433\u0434\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_0 \\sim \\mathcal{N}(0,I)\" alt=\"x_0 \\sim \\mathcal{N}(0,I)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg\" width=\"100\" height=\"19\" data-width=\"12.552\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.552ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u0448\u0443\u043c, \u0430 <img decoding=\"async\" class=\"formula inline\" source=\"x_1 \\sim p_{\\text{data}}\" alt=\"x_1 \\sim p_{\\text{data}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a6\/0a64ff6c79a4951c6c607fe2c5adfc70.svg\" width=\"78\" height=\"18\" data-width=\"9.736\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 9.736ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a6\/0a64ff6c79a4951c6c607fe2c5adfc70.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a6\/0a64ff6c79a4951c6c607fe2c5adfc70.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0440\u0435\u0430\u043b\u044c\u043d\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435. \u041c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u043e\u0432\u0435\u0441\u0442\u0438 \u043f\u0440\u044f\u043c\u0443\u044e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044e:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_t = (1-t)x_0 + t x_1.\" alt=\"x_t = (1-t)x_0 + t x_1.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/af7\/af7634f1eb70ddfdd13723fc02010be5.svg\" width=\"163\" height=\"18\" data-width=\"20.325\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 20.325ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/af7\/af7634f1eb70ddfdd13723fc02010be5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/af7\/af7634f1eb70ddfdd13723fc02010be5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041c\u044b \u043c\u043e\u0436\u0435\u043c \u0441\u043e\u0435\u0434\u0438\u043d\u0438\u0442\u044c \u0432\u0441\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_0 \\sim p(x_0)\" alt=\"x_0 \\sim p(x_0)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6a1\/6a1e67bbf6845122e5b53af42a8e261a.svg\" width=\"84\" height=\"18\" data-width=\"10.479\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 10.479ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6a1\/6a1e67bbf6845122e5b53af42a8e261a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6a1\/6a1e67bbf6845122e5b53af42a8e261a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u043e \u0432\u0441\u0435\u043c\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1 \\sim p(x_1)\" alt=\"x_1 \\sim p(x_1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/16\/16a\/16afc672b26d58b2d20566d4f52c5b0b.svg\" width=\"84\" height=\"18\" data-width=\"10.479\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 10.479ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" 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https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0422\u043e \u0435\u0441\u0442\u044c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043f\u043e\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0438\u0437 \u0440\u0430\u0437\u043d\u044b\u0445 \u043f\u0430\u0440: \u0448\u0443\u043c\u044b <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       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https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0418\u0442\u043e\u0433\u043e\u0432\u0443\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u(x_t, t)\" alt=\"u(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg\" width=\"55\" height=\"18\" data-width=\"6.936\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.936ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u043e\u0436\u043d\u043e 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loading=\"lazy\" decode=\"async\"\/> \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u(x_t, t)\" alt=\"u(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg\" width=\"55\" height=\"18\" data-width=\"6.936\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.936ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c02\/c02482d8ab31bc19cee4092333f03558.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0447\u0435\u0440\u0435\u0437 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"x_1 - x_0\" alt=\"x_1 - x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg\" width=\"59\" height=\"14\" data-width=\"7.329\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 7.329ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e \u0432\u0441\u0435\u043c \u043f\u0430\u0440\u0430\u043c <img decoding=\"async\" class=\"formula inline\" source=\"x_0, x_1\" alt=\"x_0, x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/057\/0578eb4988c85891fd365ff71c1e66d5.svg\" width=\"45\" height=\"12\" data-width=\"5.57\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 5.57ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/057\/0578eb4988c85891fd365ff71c1e66d5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/057\/0578eb4988c85891fd365ff71c1e66d5.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0418\u0442\u0430\u043a, Flow Matching \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u0447\u0442\u043e \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0442\u044c \u0441\u0440\u0435\u0434\u043d\u044e\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432\u0441\u0435\u0445 \u0447\u0430\u0441\u0442\u0438\u0446, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0442 \u0447\u0435\u0440\u0435\u0437 \u044d\u0442\u0443 \u0442\u043e\u0447\u043a\u0443 \u0432 \u0434\u0430\u043d\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0434\u043b\u044f \u0438\u0441\u043a\u043e\u043c\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439. \u0424\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u044d\u0442\u043e \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0447\u0435\u0440\u0435\u0437 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u043c\u0430\u0442\u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^*(x,t) = \\mathbb{E}_{x_0,x_1} \\left[ x_1 - x_0 \\mid x_t = x \\right].\" alt=\"u^*(x,t) = \\mathbb{E}_{x_0,x_1} \\left[ x_1 - x_0 \\mid x_t = x \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg\" width=\"267\" height=\"19\" data-width=\"33.394\" data-height=\"2.347\" data-vertical-align=\"-0.608\" style=\"width: 33.394ex; height: 2.347ex; vertical-align: -0.608ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<details class=\"spoiler\">\n<summary>\u0423\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435<\/summary>\n<div class=\"spoiler__content\">\n<p><strong>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435<\/strong> \u2014 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432. \u041d\u043e \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e \u043c\u043d\u043e\u0433\u043e. \u041a\u0430\u043a \u0438 \u0432 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \ud83d\ude42<\/p>\n<p><strong>\u0423\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435<\/strong> \u2014 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u0438 \u043a\u0430\u043a\u0438\u0445-\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u0445. \u041a \u043f\u0440\u0438\u043c\u0435\u0440\u0443, \u0435\u0441\u043b\u0438 \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043d\u0430\u0439\u0442\u0438 \u0441\u0440\u0435\u0434\u043d\u044e\u044e \u043f\u0440\u043e\u0434\u043e\u043b\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u0441\u043d\u0430 \u043f\u0435\u0440\u0435\u0434 \u0441\u0435\u0441\u0441\u0438\u0435\u0439, \u0442\u043e \u0441\u0435\u0441\u0441\u0438\u044f \u2014 \u044d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435.<\/p>\n<p>\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0432\u044b\u0448\u0435 \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435: \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0432\u0441\u0435 \u043f\u0430\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"x_0,x_1\" alt=\"x_0,x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/95\/956\/956d6946953abfe9159952738cfe9288.svg\" width=\"45\" height=\"12\" data-width=\"5.57\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 5.57ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/95\/956\/956d6946953abfe9159952738cfe9288.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/95\/956\/956d6946953abfe9159952738cfe9288.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0434\u043b\u044f \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u043a\u0430\u0437\u0430\u043b\u0430\u0441\u044c \u0440\u0430\u0432\u043d\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0431\u0435\u0440\u0451\u043c \u0438\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1-x_0\" alt=\"x_1-x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/847\/84794f66c2f166b6ee3f35a7de4e013d.svg\" width=\"59\" height=\"14\" data-width=\"7.329\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 7.329ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/847\/84794f66c2f166b6ee3f35a7de4e013d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/847\/84794f66c2f166b6ee3f35a7de4e013d.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0443\u0441\u0440\u0435\u0434\u043d\u044f\u0435\u043c. \u041f\u043e\u043b\u0443\u0447\u0438\u0432\u0448\u0435\u0435\u0441\u044f \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u0435\u0441\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0415\u0433\u043e \u043c\u044b \u0438 \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f.<\/p>\n<\/div>\n<\/details>\n<p>\u0417\u0434\u0435\u0441\u044c \u0432\u0440\u0435\u043c\u044f <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043e: \u043c\u044b \u0443\u0441\u0440\u0435\u0434\u043d\u044f\u0435\u043c \u043f\u043e \u043f\u0430\u0440\u0430\u043c <img decoding=\"async\" class=\"formula inline\" source=\"(x_0,x_1)\" alt=\"(x_0,x_1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg\" width=\"59\" height=\"18\" data-width=\"7.33\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.33ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432 \u044d\u0442\u043e\u0442 \u043c\u043e\u043c\u0435\u043d\u0442 \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0442 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u043d\u0435 \u043f\u043e \u0440\u0430\u0437\u043d\u044b\u043c \u043c\u043e\u043c\u0435\u043d\u0442\u0430\u043c \u0432\u0440\u0435\u043c\u0435\u043d\u0438.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/9ef\/2b5\/244\/9ef2b5244d98fe0784222d6e6bf38d58.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 12. \u041f\u0440\u043e\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u043e\u0442 \u0440\u0430\u0437\u043d\u044b\u0445 \u043f\u0430\u0440 (x_0,x_1) \u0432 \u043e\u0434\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435; \u043f\u043e\u043b\u0435 u^*(x,t) \u0431\u0435\u0440\u0451\u0442 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439, \u0430 \u043c\u044b \u0432 \u0438\u0442\u043e\u0433\u0435 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0438\u0441\u043a\u043e\u043c\u0443\u044e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044e\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/9ef\/2b5\/244\/9ef2b5244d98fe0784222d6e6bf38d58.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/9ef\/2b5\/244\/9ef2b5244d98fe0784222d6e6bf38d58.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 12. \u041f\u0440\u043e\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u043e\u0442 \u0440\u0430\u0437\u043d\u044b\u0445 \u043f\u0430\u0440 (x_0,x_1) \u0432 \u043e\u0434\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435; \u043f\u043e\u043b\u0435 u^*(x,t) \u0431\u0435\u0440\u0451\u0442 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439, \u0430 \u043c\u044b \u0432 \u0438\u0442\u043e\u0433\u0435 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0438\u0441\u043a\u043e\u043c\u0443\u044e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044e<\/figcaption><\/div>\n<\/figure>\n<p>\u041f\u0440\u044f\u043c\u044b\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043f\u0440\u0438 \u0441\u043e\u0435\u0434\u0438\u043d\u0435\u043d\u0438\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043f\u0440\u0438 \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 \u2014 \u043d\u0435 \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435. \u041f\u0440\u043e\u0441\u0442\u043e \u043d\u0430\u043c \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0443\u0447\u0438\u0442\u044c \u043d\u0435 \u0432\u0441\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0438\u0435 \u0447\u0435\u0440\u0435\u0437 \u0442\u0435\u043a\u0443\u0449\u0443\u044e \u0442\u043e\u0447\u043a\u0443, \u0430 \u0438\u0445 \u0441\u0440\u0435\u0434\u043d\u0435\u0435.<\/p>\n<p>\u041f\u043e\u0447\u0435\u043c\u0443 \u043c\u043e\u0436\u043d\u043e \u0431\u0440\u0430\u0442\u044c \u0438\u043c\u0435\u043d\u043d\u043e \u0441\u0440\u0435\u0434\u043d\u0435\u0435? \u0418\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e, \u043d\u0430\u0441 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0443\u0435\u0442 \u043d\u0435 \u0441\u0443\u0434\u044c\u0431\u0430 \u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u0438\u0446\u044b, \u0430 \u0442\u043e, \u043a\u0430\u043a \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0432\u0441\u0451 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0442\u043e\u0447\u0435\u043a. <strong>\u0415\u0441\u043b\u0438 \u0447\u0435\u0440\u0435\u0437 \u043e\u0434\u043d\u0443 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430 \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u043c\u043d\u043e\u0433\u043e \u0447\u0430\u0441\u0442\u0438\u0446 \u0441 \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044f\u043c\u0438, \u0442\u043e \u043e\u0431\u0449\u0435\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0438\u0445 \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u043f\u043e\u0442\u043e\u043a\u043e\u043c.<\/strong> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0432\u044b\u0443\u0447\u0438\u0442\u044c \u043d\u0435 \u043a\u0430\u0436\u0434\u0443\u044e \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u0443\u044e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044e, \u0430 \u0443\u0441\u0440\u0435\u0434\u043d\u0451\u043d\u043d\u043e\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u^*(x,t)\" alt=\"u^*(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg\" width=\"57\" height=\"18\" data-width=\"7.159\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.159ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u041d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u043c\u044b \u043e\u0431\u0443\u0447\u0430\u0435\u043c \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_{\\theta}(x,t)\" alt=\"u_{\\theta}(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg\" width=\"57\" height=\"18\" data-width=\"7.109\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.109ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0442\u044c \u043f\u043e\u043b\u0435. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u043f\u0430\u0440\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x_0,x_1\" alt=\"x_0,x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/95\/956\/956d6946953abfe9159952738cfe9288.svg\" width=\"45\" height=\"12\" data-width=\"5.57\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 5.57ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/95\/956\/956d6946953abfe9159952738cfe9288.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/95\/956\/956d6946953abfe9159952738cfe9288.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0441\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x_t = (1-t)x_0 + t x_1\" alt=\"x_t = (1-t)x_0 + t x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5b\/5b5\/5b5b1567db59db5e87e1d8c73edd87bb.svg\" width=\"158\" height=\"18\" data-width=\"19.696\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 19.696ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5b\/5b5\/5b5b1567db59db5e87e1d8c73edd87bb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5b\/5b5\/5b5b1567db59db5e87e1d8c73edd87bb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u043f\u0440\u043e\u0441\u0438\u043c \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"x_t,t\" alt=\"x_t,t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03f\/03f1b5da699f899a34c17419628ee48a.svg\" width=\"31\" height=\"15\" data-width=\"3.882\" data-height=\"1.855\" data-vertical-align=\"-0.439\" style=\"width: 3.882ex; height: 1.855ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03f\/03f1b5da699f899a34c17419628ee48a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03f\/03f1b5da699f899a34c17419628ee48a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u0442\u044c \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"x_1 - x_0.\" alt=\"x_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3bd\/3bdc504732b7ddeadab4e70d6ec88e1c.svg\" width=\"64\" height=\"14\" data-width=\"7.958\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 7.958ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3bd\/3bdc504732b7ddeadab4e70d6ec88e1c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3bd\/3bdc504732b7ddeadab4e70d6ec88e1c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0431\u044b\u0447\u043d\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathcal{L}(\\theta) = \\mathbb{E}_{x_0,x_1,t} \\left[ \\left\\| u_\\theta(x_t,t) - (x_1-x_0) \\right\\|^2 \\right].\" alt=\"\\mathcal{L}(\\theta) = \\mathbb{E}_{x_0,x_1,t} \\left[ \\left\\| u_\\theta(x_t,t) - (x_1-x_0) \\right\\|^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03c\/03c1bddd5629b9bb52ee915ebfaefa61.svg\" width=\"319\" height=\"33\" data-width=\"39.912\" data-height=\"4.07\" data-vertical-align=\"-1.469\" style=\"width: 39.912ex; height: 4.07ex; vertical-align: -1.469ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03c\/03c1bddd5629b9bb52ee915ebfaefa61.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03c\/03c1bddd5629b9bb52ee915ebfaefa61.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041c\u0438\u043d\u0438\u043c\u0443\u043c \u044d\u0442\u043e\u0439 MSE-\u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u0440\u0438 \u043a\u0430\u0436\u0434\u043e\u043c \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043a\u0430\u043a \u0440\u0430\u0437 \u0438 \u0440\u0430\u0432\u0435\u043d \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u043c\u0443 \u0441\u0440\u0435\u0434\u043d\u0435\u043c\u0443:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u_{\\theta}(x,t) \\approx u^*(x,t) = \\mathbb{E}_{x_0,x_1} \\left[ x_1-x_0 \\mid x_t=x \\right].\" alt=\"u_{\\theta}(x,t) \\approx u^*(x,t) = \\mathbb{E}_{x_0,x_1} \\left[ x_1-x_0 \\mid x_t=x \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/077e93338e4730987bdef948bf122783.svg\" width=\"348\" height=\"19\" data-width=\"43.521\" data-height=\"2.347\" data-vertical-align=\"-0.608\" style=\"width: 43.521ex; height: 2.347ex; vertical-align: -0.608ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/077e93338e4730987bdef948bf122783.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/077e93338e4730987bdef948bf122783.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<details class=\"spoiler\">\n<summary>\u0423\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435<\/summary>\n<div class=\"spoiler__content\">\n<p>\u041f\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \u043c\u0438\u043d\u0438\u043c\u0443\u043c MSE-\u0437\u0430\u0434\u0430\u0447\u0438 \u0440\u0430\u0432\u0435\u043d \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u043c\u0443 \u0441\u0440\u0435\u0434\u043d\u0435\u043c\u0443.<\/p>\n<p>\u0420\u0430\u0441\u043f\u0438\u0448\u0435\u043c \u043d\u0430\u0448 \u043b\u043e\u0441\u0441 \u043a\u0430\u043a \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435 \u043e\u0442 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u044f (\u0432\u044b\u043d\u0435\u0441\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>):<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned}\\mathcal{L}(\\theta)&amp;=\\mathbb{E}_{x_0,x_1,t}\\left[\\left\\|u_\\theta(x_t,t)-(x_1-x_0)\\right\\|^2\\right] \\\\&amp;=\\mathbb{E}_{t,x_t}\\left[\\mathbb{E}_{x_0,x_1 \\mid x_t,t}\\left[\\left\\|u_\\theta(x_t,t)-(x_1-x_0)\\right\\|^2\\right]\\right].\\end{aligned}\" alt=\"\\begin{aligned}\\mathcal{L}(\\theta)&amp;=\\mathbb{E}_{x_0,x_1,t}\\left[\\left\\|u_\\theta(x_t,t)-(x_1-x_0)\\right\\|^2\\right] \\\\&amp;=\\mathbb{E}_{t,x_t}\\left[\\mathbb{E}_{x_0,x_1 \\mid x_t,t}\\left[\\left\\|u_\\theta(x_t,t)-(x_1-x_0)\\right\\|^2\\right]\\right].\\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a34\/a3445acb14292fe1cefe961dbaa3ee79.svg\" width=\"388\" height=\"71\" data-width=\"48.501\" data-height=\"8.819\" data-vertical-align=\"-3.844\" style=\"width: 48.501ex; height: 8.819ex; vertical-align: -3.844ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a34\/a3445acb14292fe1cefe961dbaa3ee79.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a34\/a3445acb14292fe1cefe961dbaa3ee79.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041e\u0442\u0434\u0435\u043b\u044c\u043d\u043e \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0438\u043c <img decoding=\"async\" class=\"formula inline\" source=\"\\mu(x_t, t)\" alt=\"\\mu(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg\" width=\"56\" height=\"18\" data-width=\"7.007\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.007ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043a\u0430\u043a \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"\\mu(x_t,t)=\\mathbb{E}_{x_0,x_1 \\mid x_t,t}\\left[x_1-x_0\\right]\" alt=\"\\mu(x_t,t)=\\mathbb{E}_{x_0,x_1 \\mid x_t,t}\\left[x_1-x_0\\right]\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/91\/913\/913fd5a87c014c4fe425fd1bef7fa836.svg\" width=\"218\" height=\"20\" data-width=\"27.28\" data-height=\"2.495\" data-vertical-align=\"-0.682\" style=\"width: 27.28ex; height: 2.495ex; vertical-align: -0.682ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/91\/913\/913fd5a87c014c4fe425fd1bef7fa836.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/91\/913\/913fd5a87c014c4fe425fd1bef7fa836.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041c\u044b \u0445\u043e\u0442\u0438\u043c \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"u_\\theta(x_t, t)\" alt=\"u_\\theta(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg\" width=\"63\" height=\"18\" data-width=\"7.875\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.875ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043a\u0430\u043a \u0440\u0430\u0437 \u0432\u044b\u0443\u0447\u0438\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"\\mu(x_t, t)\" alt=\"\\mu(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg\" width=\"56\" height=\"18\" data-width=\"7.007\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.007ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0420\u0430\u0441\u043f\u0438\u0448\u0435\u043c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e \u0442\u043e, \u0447\u0442\u043e \u0441\u0442\u043e\u0438\u0442 \u043f\u043e\u0434 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} &amp; \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| u_\\theta(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;= \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) + \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;= \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 \\right] \\\\ &amp;\\quad + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;\\quad + 2 \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\langle u_\\theta(x_t,t)-\\mu(x_t,t), \\mu(x_t,t)-(x_1-x_0) \\right\\rangle \\right] \\\\ &amp;= \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;\\quad + 2 \\left\\langle u_\\theta(x_t,t)-\\mu(x_t,t), \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\mu(x_t,t)-(x_1-x_0) \\right] \\right\\rangle \\\\ &amp;= \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;\\quad + 2 \\left\\langle u_\\theta(x_t,t)-\\mu(x_t,t), \\mu(x_t,t) - \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[x_1-x_0 \\right] \\right\\rangle \\\\ &amp;= \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;\\quad + 2 \\left\\langle u_\\theta(x_t,t)-\\mu(x_t,t), \\mu(x_t,t) - \\mu(x_t, t) \\right\\rangle \\\\ &amp;= \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;= \\left\\| u_\\theta(x_t,t) - \\mu(x_t,t) \\right\\|^2 + \\operatorname{tr} \\operatorname{Cov}_{x_0,x_1 \\mid x_t,t}(x_1-x_0). \\end{aligned}\" alt=\"\\begin{aligned} &amp; \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| u_\\theta(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;= \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) + \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;= \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 \\right] \\\\ &amp;\\quad + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;\\quad + 2 \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\langle u_\\theta(x_t,t)-\\mu(x_t,t), \\mu(x_t,t)-(x_1-x_0) \\right\\rangle \\right] \\\\ &amp;= \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;\\quad + 2 \\left\\langle u_\\theta(x_t,t)-\\mu(x_t,t), \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\mu(x_t,t)-(x_1-x_0) \\right] \\right\\rangle \\\\ &amp;= \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;\\quad + 2 \\left\\langle u_\\theta(x_t,t)-\\mu(x_t,t), \\mu(x_t,t) - \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[x_1-x_0 \\right] \\right\\rangle \\\\ &amp;= \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;\\quad + 2 \\left\\langle u_\\theta(x_t,t)-\\mu(x_t,t), \\mu(x_t,t) - \\mu(x_t, t) \\right\\rangle \\\\ &amp;= \\left\\| u_\\theta(x_t,t)-\\mu(x_t,t) \\right\\|^2 + \\mathbb{E}_{x_0,x_1 \\mid x_t,t} \\left[ \\left\\| \\mu(x_t,t)-(x_1-x_0) \\right\\|^2 \\right] \\\\ &amp;= \\left\\| u_\\theta(x_t,t) - \\mu(x_t,t) \\right\\|^2 + \\operatorname{tr} \\operatorname{Cov}_{x_0,x_1 \\mid x_t,t}(x_1-x_0). \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/96\/961\/9610c77f480fb69967307072a6d590b0.svg\" width=\"477\" height=\"431\" data-width=\"59.596\" data-height=\"53.849\" data-vertical-align=\"-26.359\" style=\"width: 59.596ex; height: 53.849ex; vertical-align: -26.359ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/96\/961\/9610c77f480fb69967307072a6d590b0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/96\/961\/9610c77f480fb69967307072a6d590b0.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412 \u0438\u0442\u043e\u0433\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u043c, \u0447\u0442\u043e \u043e\u043f\u0442\u0438\u043c\u0443\u043c \u0443 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\theta(x_t, t)\" alt=\"u_\\theta(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg\" width=\"63\" height=\"18\" data-width=\"7.875\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.875ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0440\u0430\u0432\u0435\u043d <img decoding=\"async\" class=\"formula inline\" source=\"\\mu(x_t, t)\" alt=\"\\mu(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg\" width=\"56\" height=\"18\" data-width=\"7.007\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.007ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4e\/e4eebdf559150129eb9ef1a18ce3ab82.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u0430\u043a \u043a\u0430\u043a \u0432\u0442\u043e\u0440\u043e\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 \u043d\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\theta\" alt=\"u_\\theta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg\" width=\"18\" height=\"18\" data-width=\"2.232\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.232ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0427\u0442\u043e \u043c\u044b \u0438 \u0445\u043e\u0442\u0435\u043b\u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c.<\/p>\n<\/div>\n<\/details>\n<p>\u0418\u043c\u0435\u043d\u043d\u043e \u043f\u043e\u044d\u0442\u043e\u043c\u0443 Flow Matching \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u0443\u0447\u0430\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u043e: \u043c\u044b \u0441\u0430\u043c\u0438 \u0441\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0437\u043d\u0430\u0435\u043c \u0446\u0435\u043b\u0435\u0432\u0443\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"x_1-x_0\" alt=\"x_1-x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/847\/84794f66c2f166b6ee3f35a7de4e013d.svg\" width=\"59\" height=\"14\" data-width=\"7.329\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 7.329ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/847\/84794f66c2f166b6ee3f35a7de4e013d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/847\/84794f66c2f166b6ee3f35a7de4e013d.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0435\u0439 \u043f\u0430\u0440\u044b.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/a83\/8cd\/69a\/a838cd69ab9dce54343ef8acb4ca72e6.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 13. \u041f\u0435\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u043a \u043f\u043e\u043b\u044e: \u0432 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043c\u043d\u043e\u0433\u043e \u0441\u0435\u043c\u043f\u043b\u043e\u0432\u044b\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439, \u0443\u0441\u0440\u0435\u0434\u043d\u044f\u0435\u043c \u0438\u0445 \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u0442\u0440\u0435\u043b\u043a\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/a83\/8cd\/69a\/a838cd69ab9dce54343ef8acb4ca72e6.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/a83\/8cd\/69a\/a838cd69ab9dce54343ef8acb4ca72e6.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 13. \u041f\u0435\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u043a \u043f\u043e\u043b\u044e: \u0432 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043c\u043d\u043e\u0433\u043e \u0441\u0435\u043c\u043f\u043b\u043e\u0432\u044b\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439, \u0443\u0441\u0440\u0435\u0434\u043d\u044f\u0435\u043c \u0438\u0445 \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u0442\u0440\u0435\u043b\u043a\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f<\/figcaption><\/div>\n<\/figure>\n<p>\u0412 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0442\u0440\u0451\u0445 \u0441\u043a\u0440\u044b\u0442\u044b\u0445 \u0431\u043b\u043e\u043a\u0430\u0445 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 Flow Matching\u2019\u0430 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0435 \u043f\u0435\u0440\u0435\u0432\u043e\u0434\u0430 \u043e\u0434\u043d\u043e\u0433\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432 \u0434\u0432\u0430, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u0435\u0435 \u043f\u043e\u0447\u0438\u0442\u0430\u0442\u044c \u043f\u0440\u043e \u0438\u043d\u0442\u0443\u0438\u0446\u0438\u044e \u043c\u0435\u0442\u043e\u0434\u0430.<\/p>\n<details class=\"spoiler\">\n<summary>\u041f\u0435\u0440\u0435\u0432\u043e\u0434 \u043e\u0434\u043d\u043e\u0439 \u0433\u0430\u0443\u0441\u0441\u0438\u0430\u043d\u044b \u0432 \u0434\u0432\u0435<\/summary>\n<div class=\"spoiler__content\">\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u0441 \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435\u043c \u043e\u0434\u043d\u043e\u0433\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432 \u0441\u043c\u0435\u0441\u044c \u0434\u0432\u0443\u0445 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439. \u0414\u043b\u044f \u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u043c \u0441\u0435\u043c\u043f\u043b\u044b \u0438\u0437 <img decoding=\"async\" class=\"formula inline\" source=\"x_0 \\sim p_0\" alt=\"x_0 \\sim p_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/422\/42222cecd2a2556d55cfb4fc71e7f9f7.svg\" width=\"59\" height=\"18\" data-width=\"7.425\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.425ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/422\/42222cecd2a2556d55cfb4fc71e7f9f7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/422\/42222cecd2a2556d55cfb4fc71e7f9f7.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1 \\sim p_1\" alt=\"x_1 \\sim p_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/33\/33d\/33df5b10477b64bab7fc86e42d9359a6.svg\" width=\"59\" height=\"18\" data-width=\"7.425\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.425ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/33\/33d\/33df5b10477b64bab7fc86e42d9359a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/33\/33d\/33df5b10477b64bab7fc86e42d9359a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0441\u0435\u043c\u043f\u043b\u044b <img decoding=\"async\" class=\"formula inline\" source=\"x_t \\sim p_t\" alt=\"x_t \\sim p_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/018\/018984e2b17f6c959ada2eabc1bf10e6.svg\" width=\"56\" height=\"18\" data-width=\"6.98\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.98ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/018\/018984e2b17f6c959ada2eabc1bf10e6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/018\/018984e2b17f6c959ada2eabc1bf10e6.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0431\u044b\u043b\u0438 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u044b \u043a\u0430\u043a <img decoding=\"async\" class=\"formula inline\" source=\"x_t = (1 - t)x_0 + t x_1\" alt=\"x_t = (1 - t)x_0 + t x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec1\/ec1ab4d87ff94b4b0773fa83402a1484.svg\" width=\"158\" height=\"18\" data-width=\"19.696\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 19.696ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec1\/ec1ab4d87ff94b4b0773fa83402a1484.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ec\/ec1\/ec1ab4d87ff94b4b0773fa83402a1484.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/704\/07c\/1eb\/70407c1ebeed97e1d2109eb1175c7d42.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 14. \u0418\u0433\u0440\u0443\u0448\u0435\u0447\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0441 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u043c\u0438 \u0433\u0430\u0443\u0441\u0441\u0438\u0430\u043d\u0430\u043c\u0438: \u0441\u0435\u043c\u043f\u043b\u044b \u0438\u0437 \u043e\u0434\u043d\u043e\u0433\u043e \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0433\u0430\u0443\u0441\u0441\u0438\u0430\u043d\u0430 \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u044f\u0442 \u043a \u0441\u043c\u0435\u0441\u0438 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0433\u0430\u0443\u0441\u0441\u0438\u0430\u043d\u043e\u0432\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/704\/07c\/1eb\/70407c1ebeed97e1d2109eb1175c7d42.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/704\/07c\/1eb\/70407c1ebeed97e1d2109eb1175c7d42.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 14. \u0418\u0433\u0440\u0443\u0448\u0435\u0447\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0441 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u043c\u0438 \u0433\u0430\u0443\u0441\u0441\u0438\u0430\u043d\u0430\u043c\u0438: \u0441\u0435\u043c\u043f\u043b\u044b \u0438\u0437 \u043e\u0434\u043d\u043e\u0433\u043e \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0433\u0430\u0443\u0441\u0441\u0438\u0430\u043d\u0430 \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u044f\u0442 \u043a \u0441\u043c\u0435\u0441\u0438 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0433\u0430\u0443\u0441\u0441\u0438\u0430\u043d\u043e\u0432<\/figcaption><\/div>\n<\/figure>\n<p>\u0414\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043d\u0430\u0439\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0435\u0451 \u043f\u043e\u0440\u043e\u0434\u0438\u043b\u0438, \u0438 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0443\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"x_1 - x_0\" alt=\"x_1 - x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg\" width=\"59\" height=\"14\" data-width=\"7.329\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 7.329ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 781w\" loading=\"lazy\" decode=\"async\"\/> (\u043d\u0430 \u0440\u0438\u0441\u0443\u043d\u043a\u0435 \u0434\u043b\u044f \u0443\u0434\u043e\u0431\u0441\u0442\u0432\u0430 \u0432\u043e\u0441\u043f\u0440\u0438\u044f\u0442\u0438\u044f \u043c\u044b \u0443\u0436\u0430\u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043f\u043e \u0434\u043b\u0438\u043d\u0435).<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/992\/1b3\/cad\/9921b3cad74af63977bc493c420d276e.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 15. \u0422\u0435 \u0436\u0435 \u0441\u0435\u043c\u043f\u043b\u044b \u0432 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442: \u0443 \u043a\u0430\u0436\u0434\u043e\u0439 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0435\u0439 \u043f\u0430\u0440\u044b \u0435\u0441\u0442\u044c \u0441\u0432\u043e\u044f \u0441\u0435\u043c\u043f\u043b\u043e\u0432\u0430\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0438\u0437 \u043f\u043e\u0445\u043e\u0436\u0438\u0445 \u0442\u043e\u0447\u0435\u043a \u043c\u043e\u0433\u0443\u0442 \u0432\u044b\u0445\u043e\u0434\u0438\u0442\u044c \u0440\u0430\u0437\u043d\u044b\u0435 \u0441\u0442\u0440\u0435\u043b\u043a\u0438\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/992\/1b3\/cad\/9921b3cad74af63977bc493c420d276e.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/992\/1b3\/cad\/9921b3cad74af63977bc493c420d276e.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 15. \u0422\u0435 \u0436\u0435 \u0441\u0435\u043c\u043f\u043b\u044b \u0432 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442: \u0443 \u043a\u0430\u0436\u0434\u043e\u0439 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0435\u0439 \u043f\u0430\u0440\u044b \u0435\u0441\u0442\u044c \u0441\u0432\u043e\u044f \u0441\u0435\u043c\u043f\u043b\u043e\u0432\u0430\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0438\u0437 \u043f\u043e\u0445\u043e\u0436\u0438\u0445 \u0442\u043e\u0447\u0435\u043a \u043c\u043e\u0433\u0443\u0442 \u0432\u044b\u0445\u043e\u0434\u0438\u0442\u044c \u0440\u0430\u0437\u043d\u044b\u0435 \u0441\u0442\u0440\u0435\u043b\u043a\u0438<\/figcaption><\/div>\n<\/figure>\n<p>\u0418\u0442\u043e\u0433\u043e\u0432\u0430\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043b\u044f \u0442\u043e\u0447\u043a\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u0441\u0440\u0435\u0434\u0438 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"x_1 - x_0\" alt=\"x_1 - x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg\" width=\"59\" height=\"14\" data-width=\"7.329\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 7.329ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4e\/4ed\/4ed34ffa6e6e06493326ad9e9cfc9656.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0434\u043b\u044f \u043a\u043e\u0442\u043e\u0440\u044b\u0445 <img decoding=\"async\" class=\"formula inline\" source=\"x_t = x\" alt=\"x_t = x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7c\/7cc\/7cc5bb6d485d22efc07573e98f551871.svg\" width=\"51\" height=\"13\" data-width=\"6.371\" data-height=\"1.676\" data-vertical-align=\"-0.357\" style=\"width: 6.371ex; height: 1.676ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7c\/7cc\/7cc5bb6d485d22efc07573e98f551871.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7c\/7cc\/7cc5bb6d485d22efc07573e98f551871.svg 781w\" loading=\"lazy\" decode=\"async\"\/> (\u0434\u043b\u044f \u0443\u0434\u043e\u0431\u0441\u0442\u0432\u0430 \u0432\u043e\u0441\u043f\u0440\u0438\u044f\u0442\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043c\u044b \u0443\u0436\u0430\u043b\u0438 \u043f\u043e \u0434\u043b\u0438\u043d\u0435).<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/4ec\/bd0\/8ac\/4ecbd08ac0c4ad43426ec42d7b582a0b.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 16. \u041f\u043e\u0441\u043b\u0435 \u0443\u0441\u0440\u0435\u0434\u043d\u0435\u043d\u0438\u044f \u0441\u0435\u043c\u043f\u043b\u043e\u0432\u044b\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0438\u0442\u043e\u0433\u043e\u0432\u043e\u0435 \u043f\u043e\u043b\u0435: \u0432\u0435\u0440\u0445\u043d\u044f\u044f \u0447\u0430\u0441\u0442\u044c \u043f\u043e\u0442\u043e\u043a\u0430 \u0438\u0434\u0451\u0442 \u043a \u0432\u0435\u0440\u0445\u043d\u0435\u0439 \u043c\u043e\u0434\u0435, \u043d\u0438\u0436\u043d\u044f\u044f \u2014 \u043a \u043d\u0438\u0436\u043d\u0435\u0439\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/4ec\/bd0\/8ac\/4ecbd08ac0c4ad43426ec42d7b582a0b.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/4ec\/bd0\/8ac\/4ecbd08ac0c4ad43426ec42d7b582a0b.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 16. \u041f\u043e\u0441\u043b\u0435 \u0443\u0441\u0440\u0435\u0434\u043d\u0435\u043d\u0438\u044f \u0441\u0435\u043c\u043f\u043b\u043e\u0432\u044b\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0438\u0442\u043e\u0433\u043e\u0432\u043e\u0435 \u043f\u043e\u043b\u0435: \u0432\u0435\u0440\u0445\u043d\u044f\u044f \u0447\u0430\u0441\u0442\u044c \u043f\u043e\u0442\u043e\u043a\u0430 \u0438\u0434\u0451\u0442 \u043a \u0432\u0435\u0440\u0445\u043d\u0435\u0439 \u043c\u043e\u0434\u0435, \u043d\u0438\u0436\u043d\u044f\u044f \u2014 \u043a \u043d\u0438\u0436\u043d\u0435\u0439<\/figcaption><\/div>\n<\/figure>\n<\/div>\n<\/details>\n<details class=\"spoiler\">\n<summary>\u041f\u043e\u044f\u0432\u043b\u0435\u043d\u0438\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0439 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438<\/summary>\n<div class=\"spoiler__content\">\n<p>\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c, \u0447\u0442\u043e \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041e\u043d\u0430 \u043c\u043e\u0433\u043b\u0430 \u043f\u043e\u044f\u0432\u0438\u0442\u044c\u0441\u044f \u0438\u0437 \u0440\u0430\u0437\u043d\u044b\u0445 \u043f\u0430\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"(x_0, x_1)\" alt=\"(x_0, x_1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f94\/f9434cb13301342108f760c4d43b9a81.svg\" width=\"59\" height=\"18\" data-width=\"7.33\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.33ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f94\/f9434cb13301342108f760c4d43b9a81.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f94\/f9434cb13301342108f760c4d43b9a81.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0414\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u0430\u043a\u043e\u0439 \u043f\u0430\u0440\u044b \u0435\u0441\u0442\u044c \u0441\u0432\u043e\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"v = x_1 - x_0.\" alt=\"v = x_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6d\/6d5\/6d544ce6747ec7f2a49feb4625ed8e81.svg\" width=\"97\" height=\"14\" data-width=\"12.073\" data-height=\"1.694\" data-vertical-align=\"-0.375\" style=\"width: 12.073ex; height: 1.694ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6d\/6d5\/6d544ce6747ec7f2a49feb4625ed8e81.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6d\/6d5\/6d544ce6747ec7f2a49feb4625ed8e81.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u041c\u043e\u0436\u043d\u043e \u0441\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e \u043e\u043d\u0430 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435\u043c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0441\u0438\u043b\u044b, \u0442\u043e\u043b\u0447\u043a\u0430. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432 \u043e\u0434\u043d\u043e\u0439 \u0438 \u0442\u043e\u0439 \u0436\u0435 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043d\u0435 \u043e\u0434\u043d\u0430 \u00ab\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u0430\u044f \u0441\u0438\u043b\u0430\u00bb, \u0430 \u0446\u0435\u043b\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u0441\u0438\u043b.<\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0432\u043c\u0435\u0441\u0442\u043e \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u0441\u0440\u0430\u0437\u0443 \u0437\u0430\u043c\u0435\u043d\u044f\u0442\u044c \u0432\u0441\u0435 \u044d\u0442\u0438 \u0441\u0438\u043b\u044b \u043d\u0430 \u0441\u0440\u0435\u0434\u043d\u044e\u044e, \u0431\u0443\u0434\u0435\u043c \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u0442\u044c \u0438\u0445 \u043f\u043e \u043e\u0434\u043d\u043e\u0439. \u041d\u0430 \u043e\u0447\u0435\u043d\u044c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u043e\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"dt\" alt=\"dt\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg\" width=\"16\" height=\"13\" data-width=\"1.993\" data-height=\"1.595\" data-vertical-align=\"-0.025\" style=\"width: 1.993ex; height: 1.595ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" 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srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0418\u043d\u044b\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0435\u0441\u043b\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0430 \u0447\u0430\u0441\u0442\u0438\u0446\u0443 \u0434\u0435\u0439\u0441\u0442\u0432\u0443\u0435\u0442 \u043c\u043d\u043e\u0433\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u0441\u0438\u043b, \u0442\u043e \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e \u043c\u0430\u043b\u043e\u043c \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0435 \u0438\u0445 \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c \u043e\u0434\u043d\u043e\u0439 \u0441\u0440\u0435\u0434\u043d\u0435\u0439 \u0441\u0438\u043b\u043e\u0439:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^*(x,t) = \\mathbb{E}_{x_0,x_1} \\left[ x_1 - x_0 \\mid x_t = x \\right].\" alt=\"u^*(x,t) = \\mathbb{E}_{x_0,x_1} \\left[ x_1 - x_0 \\mid x_t = x \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg\" width=\"267\" height=\"19\" data-width=\"33.394\" data-height=\"2.347\" data-vertical-align=\"-0.608\" style=\"width: 33.394ex; height: 2.347ex; vertical-align: -0.608ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u043c\u0435\u043d\u043d\u043e \u044d\u0442\u043e \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0438 \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0443\u0447\u0438\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u0438. \u041e\u043d\u043e \u043d\u0435 \u043f\u044b\u0442\u0430\u0435\u0442\u0441\u044f \u0432\u043e\u0441\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u044c \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0443\u044e \u043f\u0430\u0440\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"(x_0,x_1)\" alt=\"(x_0,x_1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg\" width=\"59\" height=\"18\" data-width=\"7.33\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.33ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043f\u043e\u0442\u043e\u043a \u0447\u0430\u0441\u0442\u0438\u0446, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043f\u0435\u0440\u0435\u043d\u043e\u0441\u0438\u0442 \u0432\u0441\u0451 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0448\u0443\u043c\u0430 \u043a \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u0434\u0430\u043d\u043d\u044b\u0445.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/62b\/5fb\/c4c\/62b5fbc4c0e8b1931f76beab58b8e8f8.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 17. \u0417\u0430\u043c\u0435\u043d\u0430 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u043c\u0438\u043a\u0440\u043e\u0442\u043e\u043b\u0447\u043a\u043e\u0432 \u0432 \u0442\u043e\u0447\u043a\u0435\u00a0x \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 t\u00a0\u043d\u0430 \u043c\u0430\u043b\u043e\u043c \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0435 \u043e\u0434\u043d\u0438\u043c \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u0441\u0434\u0432\u0438\u0433\u043e\u043c\u00a0u^*(x, t)\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/62b\/5fb\/c4c\/62b5fbc4c0e8b1931f76beab58b8e8f8.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/62b\/5fb\/c4c\/62b5fbc4c0e8b1931f76beab58b8e8f8.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 17. \u0417\u0430\u043c\u0435\u043d\u0430 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u043c\u0438\u043a\u0440\u043e\u0442\u043e\u043b\u0447\u043a\u043e\u0432 \u0432 \u0442\u043e\u0447\u043a\u0435\u00a0x \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 t\u00a0\u043d\u0430 \u043c\u0430\u043b\u043e\u043c \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0435 \u043e\u0434\u043d\u0438\u043c \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u0441\u0434\u0432\u0438\u0433\u043e\u043c\u00a0u^*(x, t)<\/figcaption><\/div>\n<\/figure>\n<\/div>\n<\/details>\n<details class=\"spoiler\">\n<summary>\u041c\u0435\u0445\u0430\u043d\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u044f<\/summary>\n<div class=\"spoiler__content\">\n<p>\u042d\u0442\u0443 \u0438\u0434\u0435\u044e \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u0435\u0445\u0430\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0438. \u041f\u0443\u0441\u0442\u044c \u043a\u0430\u0436\u0434\u0430\u044f \u043f\u0430\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"(x_0, x_1)\" alt=\"(x_0, x_1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f94\/f9434cb13301342108f760c4d43b9a81.svg\" width=\"59\" height=\"18\" data-width=\"7.33\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.33ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f94\/f9434cb13301342108f760c4d43b9a81.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f94\/f9434cb13301342108f760c4d43b9a81.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0437\u0430\u0434\u0430\u0451\u0442 \u043e\u0434\u0438\u043d \u00ab\u0443\u0434\u0430\u0440 \u043f\u043e \u043c\u044f\u0447\u0443\u00bb: \u0444\u0443\u0442\u0431\u043e\u043b\u0438\u0441\u0442 \u0441\u0442\u043e\u0438\u0442 \u0432 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" 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\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0427\u0435\u0440\u0435\u0437 \u043d\u0435\u0451 \u043c\u043e\u0433\u0443\u0442 \u043f\u0440\u043e\u043b\u0435\u0442\u0430\u0442\u044c \u043c\u044f\u0447\u0438, \u0437\u0430\u043f\u0443\u0449\u0435\u043d\u043d\u044b\u0435 \u0438\u0437 \u0440\u0430\u0437\u043d\u044b\u0445 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0440\u0430\u0437\u043d\u044b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432 \u043e\u0434\u043d\u043e\u0439 \u0438 \u0442\u043e\u0439 \u0436\u0435 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043c\u043d\u043e\u0433\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439: \u043e\u0434\u0438\u043d \u043c\u044f\u0447 \u043b\u0435\u0442\u0438\u0442 \u0447\u0443\u0442\u044c \u043b\u0435\u0432\u0435\u0435, \u0434\u0440\u0443\u0433\u043e\u0439 \u2014 \u0447\u0443\u0442\u044c \u043f\u0440\u0430\u0432\u0435\u0435, \u0442\u0440\u0435\u0442\u0438\u0439 \u2014 \u043f\u043e\u0447\u0442\u0438 \u043f\u0440\u044f\u043c\u043e.<\/p>\n<p>\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c, \u0447\u0442\u043e \u0432 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0442\u044f\u0436\u0451\u043b\u043e\u0435 \u043f\u043e\u0434\u0432\u0438\u0436\u043d\u043e\u0435 \u0437\u0430\u0433\u0440\u0430\u0436\u0434\u0435\u043d\u0438\u0435. \u041a\u043e\u0433\u0434\u0430 \u0447\u0435\u0440\u0435\u0437 \u043d\u0435\u0433\u043e \u043f\u0440\u043e\u043b\u0435\u0442\u0430\u044e\u0442 \u043c\u044f\u0447\u0438, \u043e\u043d\u0438 \u0441\u043b\u0435\u0433\u043a\u0430 \u0435\u0433\u043e \u0442\u043e\u043b\u043a\u0430\u044e\u0442. \u041a\u0430\u0436\u0434\u044b\u0439 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0439 \u0442\u043e\u043b\u0447\u043e\u043a \u043e\u0447\u0435\u043d\u044c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0439: \u0437\u0430 \u043a\u043e\u0440\u043e\u0442\u043a\u043e\u0435 \u0432\u0440\u0435\u043c\u044f <img decoding=\"async\" class=\"formula inline\" source=\"dt\" alt=\"dt\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg\" width=\"16\" height=\"13\" data-width=\"1.993\" data-height=\"1.595\" data-vertical-align=\"-0.025\" style=\"width: 1.993ex; height: 1.595ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0437\u0430\u0433\u0440\u0430\u0436\u0434\u0435\u043d\u0438\u0435 \u0443\u0441\u043f\u0435\u0432\u0430\u0435\u0442 \u0441\u0434\u0432\u0438\u043d\u0443\u0442\u044c\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"dt\" alt=\"dt\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg\" width=\"16\" height=\"13\" data-width=\"1.993\" data-height=\"1.595\" data-vertical-align=\"-0.025\" style=\"width: 1.993ex; height: 1.595ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/301\/3017d911efceb27d1de6a92b70979795.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u0434\u0438\u043d \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u0443\u0434\u0430\u0440 \u043f\u043e\u0447\u0442\u0438 \u043d\u0435 \u043c\u0435\u043d\u044f\u0435\u0442 \u0435\u0433\u043e \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/6c0\/112\/aaf\/6c0112aaf67af80e2030a393012263b7.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 18. \u041c\u0435\u0445\u0430\u043d\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u044f: \u0440\u0430\u0437\u043d\u044b\u0435 \u0443\u0434\u0430\u0440\u044b \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0442 \u0447\u0435\u0440\u0435\u0437 \u043e\u0434\u043d\u0443 \u043e\u0431\u043b\u0430\u0441\u0442\u044c, \u0430 \u0437\u0430\u0433\u0440\u0430\u0436\u0434\u0435\u043d\u0438\u0435 \u0441\u0434\u0432\u0438\u0433\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e \u0442\u043e\u043b\u0447\u043a\u0430\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/6c0\/112\/aaf\/6c0112aaf67af80e2030a393012263b7.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/6c0\/112\/aaf\/6c0112aaf67af80e2030a393012263b7.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 18. \u041c\u0435\u0445\u0430\u043d\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u044f: \u0440\u0430\u0437\u043d\u044b\u0435 \u0443\u0434\u0430\u0440\u044b \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0442 \u0447\u0435\u0440\u0435\u0437 \u043e\u0434\u043d\u0443 \u043e\u0431\u043b\u0430\u0441\u0442\u044c, \u0430 \u0437\u0430\u0433\u0440\u0430\u0436\u0434\u0435\u043d\u0438\u0435 \u0441\u0434\u0432\u0438\u0433\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e \u0442\u043e\u043b\u0447\u043a\u0430<\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u043e \u0435\u0441\u043b\u0438 \u0437\u0430 \u044d\u0442\u043e \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u043c\u043d\u043e\u0433\u043e \u043c\u044f\u0447\u0435\u0439 \u0441 \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044f\u043c\u0438, \u0442\u043e \u0441\u0443\u043c\u043c\u0430\u0440\u043d\u044b\u0439 \u044d\u0444\u0444\u0435\u043a\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435 \u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c\u044e, \u0430 \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435\u043c \u0432\u0441\u0435\u0445 \u044d\u0442\u0438\u0445 \u043c\u0438\u043a\u0440\u043e\u0442\u043e\u043b\u0447\u043a\u043e\u0432. \u0422\u043e \u0435\u0441\u0442\u044c \u0437\u0430\u0433\u0440\u0430\u0436\u0434\u0435\u043d\u0438\u0435 \u0431\u0443\u0434\u0435\u0442 \u0434\u0432\u0438\u0433\u0430\u0442\u044c\u0441\u044f \u0442\u0430\u043a, \u043a\u0430\u043a \u0435\u0441\u043b\u0438 \u0431\u044b \u043d\u0430 \u043d\u0435\u0433\u043e \u0434\u0435\u0439\u0441\u0442\u0432\u043e\u0432\u0430\u043b\u0430 \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432\u0441\u0435\u0445 \u043c\u044f\u0447\u0435\u0439, \u043f\u0440\u043e\u043b\u0435\u0442\u0430\u044e\u0449\u0438\u0445 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> (\u0435\u0441\u043b\u0438 \u0431\u044b \u00ab\u0437\u0430\u043f\u0443\u043b\u044c\u043d\u0443\u043b\u0438\u00bb \u0432\u0441\u0435 \u043c\u044f\u0447\u0438 \u0441\u0440\u0430\u0437\u0443).<\/p>\n<p>\u0418\u043c\u0435\u043d\u043d\u043e \u044d\u0442\u0430 \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0438 \u0437\u0430\u0434\u0430\u0451\u0442 \u043f\u043e\u043b\u0435 Flow Matching\u2019\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^*(x,t) = \\mathbb{E}_{x_0,x_1} \\left[ x_1 - x_0 \\mid x_t = x \\right].\" alt=\"u^*(x,t) = \\mathbb{E}_{x_0,x_1} \\left[ x_1 - x_0 \\mid x_t = x \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg\" width=\"267\" height=\"19\" data-width=\"33.394\" data-height=\"2.347\" data-vertical-align=\"-0.608\" style=\"width: 33.394ex; height: 2.347ex; vertical-align: -0.608ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/98\/98e\/98e6b555650b55bbc427d1a3dfb9b3ce.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e \u0435\u0441\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c \u043d\u0435 \u043f\u044b\u0442\u0430\u0435\u0442\u0441\u044f \u043f\u043e\u043d\u044f\u0442\u044c, \u043a\u0430\u043a\u043e\u0439 \u0438\u043c\u0435\u043d\u043d\u043e \u043c\u044f\u0447 \u0441\u0435\u0439\u0447\u0430\u0441 \u043f\u0440\u043e\u043b\u0435\u0442\u0435\u043b \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0412\u043c\u0435\u0441\u0442\u043e \u044d\u0442\u043e\u0433\u043e \u043e\u043d\u0430 \u0443\u0447\u0438\u0442\u0441\u044f \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0442\u044c \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u0442\u043e\u043b\u0447\u043e\u043a \u043e\u0442 \u0432\u0441\u0435\u0445 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u043c\u044f\u0447\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0433\u043b\u0438 \u043e\u043a\u0430\u0437\u0430\u0442\u044c\u0441\u044f \u0432 \u0442\u043e\u0447\u043a\u0435 \u0432 \u0434\u0430\u043d\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438. \u0422\u0430\u043a\u043e\u0435 \u0443\u0441\u0440\u0435\u0434\u043d\u0451\u043d\u043d\u043e\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435 \u0438 \u043f\u0435\u0440\u0435\u043d\u043e\u0441\u0438\u0442 \u0432\u0441\u0451 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0448\u0443\u043c\u0430 \u043a \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u0434\u0430\u043d\u043d\u044b\u0445.<\/p>\n<\/div>\n<\/details>\n<h3>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c<\/h3>\n<p>\u041d\u0430 \u043a\u0430\u0436\u0434\u043e\u0439 \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u0438 \u043c\u044b \u0431\u0435\u0440\u0451\u043c \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u0448\u0443\u043c <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442 \u0438\u0437 \u0434\u0430\u043d\u043d\u044b\u0445 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0417\u0430\u0442\u0435\u043c \u0441\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 \u043c\u0435\u0436\u0434\u0443 \u0448\u0443\u043c\u043e\u043c \u0438 \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u043c \u0438 \u043f\u0440\u043e\u0441\u0438\u043c \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u0442\u044c \u0435\u0451 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c. \u041d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u0432\u0441\u0451 \u0442\u043e \u0436\u0435 \u0441\u0430\u043c\u043e\u0435 \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f \u0441\u0440\u0430\u0437\u0443 \u0434\u043b\u044f \u0446\u0435\u043b\u043e\u0433\u043e \u0431\u0430\u0442\u0447\u0430 \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043d\u0438\u0436\u0435 \u0437\u0430\u043f\u0438\u0441\u0430\u043d \u0432 \u0431\u0430\u0442\u0447\u0435\u0432\u043e\u0439 \u0444\u043e\u0440\u043c\u0435.<\/p>\n<ul>\n<li>\n<p>\u2699\ufe0f <strong>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c:<\/strong> \u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 Flow Matching-\u043c\u043e\u0434\u0435\u043b\u0438<\/p>\n<\/li>\n<li>\n<p><strong>\u0412\u0445\u043e\u0434:<\/strong> \u0421\u0435\u043c\u043f\u043b\u044b \u0438\u0437 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"p_{\\text{data}}\" alt=\"p_{\\text{data}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/84d\/84d43dc034cb736047a1e195b24d25fd.svg\" width=\"35\" height=\"18\" data-width=\"4.437\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 4.437ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/84d\/84d43dc034cb736047a1e195b24d25fd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/84\/84d\/84d43dc034cb736047a1e195b24d25fd.svg 781w\" loading=\"lazy\" decode=\"async\"\/> (\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c), \u043c\u043e\u0434\u0435\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u_\\theta\" alt=\"u_\\theta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg\" width=\"18\" height=\"18\" data-width=\"2.232\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.232ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440 \u0434\u043b\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 <img decoding=\"async\" class=\"formula inline\" source=\"\\theta\" alt=\"\\theta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/255\/2554a2bb846cffd697389e5dc8912759.svg\" width=\"12\" height=\"18\" data-width=\"1.061\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.061ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/255\/2554a2bb846cffd697389e5dc8912759.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/255\/2554a2bb846cffd697389e5dc8912759.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"N\" alt=\"N\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg\" width=\"16\" height=\"12\" data-width=\"2.009\" data-height=\"1.545\" style=\"width: 2.009ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0440\u0430\u0437\u043c\u0435\u0440 \u0431\u0430\u0442\u0447\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"B\" alt=\"B\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg\" width=\"14\" height=\"12\" data-width=\"1.717\" data-height=\"1.545\" style=\"width: 1.717ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><strong>\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/strong> \u041e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\theta \\approx u^*\" alt=\"u_\\theta \\approx u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7e\/7e4\/7e4387a89290c2bc2ce6918baee39e16.svg\" width=\"60\" height=\"18\" data-width=\"7.531\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.531ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7e\/7e4\/7e4387a89290c2bc2ce6918baee39e16.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7e\/7e4\/7e4387a89290c2bc2ce6918baee39e16.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><strong>\u0414\u043b\u044f<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"i = 1\" alt=\"i = 1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg\" width=\"39\" height=\"14\" data-width=\"4.929\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.929ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e <img decoding=\"async\" class=\"formula inline\" source=\"N\" alt=\"N\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg\" width=\"16\" height=\"12\" data-width=\"2.009\" data-height=\"1.545\" style=\"width: 2.009ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 781w\" loading=\"lazy\" decode=\"async\"\/>: <\/p>\n<ul>\n<li>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u0431\u0430\u0442\u0447 \u0448\u0443\u043c\u043e\u0432, \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432 \u0438 \u0432\u0440\u0435\u043c\u0451\u043d: <img decoding=\"async\" class=\"formula inline\" source=\"x_0^{(b)} \\sim \\mathcal{N}(0,I), \\qquad x_1^{(b)} \\sim p_{\\text{data}}, \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" alt=\"x_0^{(b)} \\sim \\mathcal{N}(0,I), \\qquad x_1^{(b)} \\sim p_{\\text{data}}, \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/00\/007\/00700d23ec9a11164f365042b4473e24.svg\" width=\"520\" height=\"25\" data-width=\"65.053\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 65.053ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/00\/007\/00700d23ec9a11164f365042b4473e24.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/00\/007\/00700d23ec9a11164f365042b4473e24.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"x_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}x_1^{(b)}\" alt=\"x_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}x_1^{(b)}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3be9a0899c143eb8aaae459be027a3c6.svg\" width=\"224\" height=\"25\" data-width=\"28.052\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 28.052ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3be9a0899c143eb8aaae459be027a3c6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3be9a0899c143eb8aaae459be027a3c6.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0446\u0435\u043b\u0435\u0432\u044b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043f\u0440\u044f\u043c\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439: <img decoding=\"async\" class=\"formula inline\" source=\"v^{(b)} \\gets x_1^{(b)} - x_0^{(b)}\" alt=\"v^{(b)} \\gets x_1^{(b)} - x_0^{(b)}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d2\/d28\/d28cca4e63b963bcaf02a65573d4ece8.svg\" width=\"131\" height=\"25\" data-width=\"16.327\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 16.327ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d2\/d28\/d28cca4e63b963bcaf02a65573d4ece8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d2\/d28\/d28cca4e63b963bcaf02a65573d4ece8.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0441\u0440\u0435\u0434\u043d\u044e\u044e \u043e\u0448\u0438\u0431\u043a\u0443 \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043f\u043e \u0431\u0430\u0442\u0447\u0443: <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L} \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\left\\| u_\\theta(x_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2\" alt=\"\\mathcal{L} \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\left\\| u_\\theta(x_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ee\/ee4\/ee41ee12e564e5ba7a9bf32167032fd6.svg\" width=\"261\" height=\"54\" data-width=\"32.646\" data-height=\"6.784\" data-vertical-align=\"-2.827\" style=\"width: 32.646ex; height: 6.784ex; vertical-align: -2.827ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ee\/ee4\/ee41ee12e564e5ba7a9bf32167032fd6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ee\/ee4\/ee41ee12e564e5ba7a9bf32167032fd6.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"\\theta\" alt=\"\\theta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/255\/2554a2bb846cffd697389e5dc8912759.svg\" width=\"12\" height=\"18\" data-width=\"1.061\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.061ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/255\/2554a2bb846cffd697389e5dc8912759.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/255\/2554a2bb846cffd697389e5dc8912759.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0448\u0430\u0433\u043e\u043c \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u0430 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}\" alt=\"\\mathcal{L}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5dc\/5dcbf640cdb155217ca0c533e1078ff7.svg\" width=\"12\" height=\"18\" data-width=\"1.561\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.561ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5dc\/5dcbf640cdb155217ca0c533e1078ff7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5dc\/5dcbf640cdb155217ca0c533e1078ff7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u041f\u043e\u0441\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_{\\theta}(x,t)\" alt=\"u_{\\theta}(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg\" width=\"57\" height=\"18\" data-width=\"7.109\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.109ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439. \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0435\u0451 \u0434\u043b\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u043d\u043e\u0432\u044b\u0445 \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432.<\/p>\n<p>\u0418\u0434\u0435\u044f \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u2014 \u043c\u044b \u0441\u0442\u0430\u0440\u0442\u0443\u0435\u043c \u0438\u0437 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0433\u043e \u0448\u0443\u043c\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_0 \\sim \\mathcal{N}(0,I)\" alt=\"x_0 \\sim \\mathcal{N}(0,I)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg\" width=\"100\" height=\"19\" data-width=\"12.552\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.552ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418 \u043f\u043e\u0441\u0442\u0435\u043f\u0435\u043d\u043d\u043e \u0434\u0432\u0438\u0433\u0430\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u043f\u043e \u0432\u044b\u0443\u0447\u0435\u043d\u043d\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u043c\u0443 \u043f\u043e\u043b\u044e \u043e\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t=0\" alt=\"t=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t=1\" alt=\"t=1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0415\u0441\u043b\u0438 \u0440\u0430\u0437\u0431\u0438\u0442\u044c \u043e\u0442\u0440\u0435\u0437\u043e\u043a <img decoding=\"async\" class=\"formula inline\" source=\"[0,1]\" alt=\"[0,1]\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/ccf\/ccfcd347d0bf65dc77afe01a3306a96b.svg\" width=\"36\" height=\"18\" data-width=\"4.526\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 4.526ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/ccf\/ccfcd347d0bf65dc77afe01a3306a96b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/ccf\/ccfcd347d0bf65dc77afe01a3306a96b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"K_{\\text{ode}}\" alt=\"K_{\\text{ode}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg\" width=\"36\" height=\"18\" data-width=\"4.508\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 4.508ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0445 \u0448\u0430\u0433\u043e\u0432, \u0442\u043e \u043e\u0434\u0438\u043d \u0448\u0430\u0433 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0442\u0430\u043a:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_{t+\\Delta t} = x_t + \\Delta t \\cdot u_\\theta(x_t,t),\" alt=\"x_{t+\\Delta t} = x_t + \\Delta t \\cdot u_\\theta(x_t,t),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/44\/440\/440a9058a777d0803ba845aa9379f2ac.svg\" width=\"207\" height=\"18\" data-width=\"25.896\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 25.896ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/44\/440\/440a9058a777d0803ba845aa9379f2ac.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/44\/440\/440a9058a777d0803ba845aa9379f2ac.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0413\u0434\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\Delta t = \\frac{1}{K_{\\text{ode}}}.\" alt=\"\\Delta t = \\frac{1}{K_{\\text{ode}}}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1dd\/1ddc1ce5294f53b05d44e22346a08e58.svg\" width=\"95\" height=\"40\" data-width=\"11.851\" data-height=\"4.945\" data-vertical-align=\"-1.907\" style=\"width: 11.851ex; height: 4.945ex; vertical-align: -1.907ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1dd\/1ddc1ce5294f53b05d44e22346a08e58.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1dd\/1ddc1ce5294f53b05d44e22346a08e58.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e \u0435\u0441\u0442\u044c \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0448\u0430\u0433\u0435 \u043c\u043e\u0434\u0435\u043b\u044c \u0433\u043e\u0432\u043e\u0440\u0438\u0442 \u043d\u0430\u043c, \u0432 \u043a\u0430\u043a\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u043d\u0443\u0436\u043d\u043e \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0441\u0434\u0432\u0438\u043d\u0443\u0442\u044c \u0442\u0435\u043a\u0443\u0449\u0443\u044e \u0442\u043e\u0447\u043a\u0443. \u041f\u043e\u0441\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"K_{\\text{ode}}\" alt=\"K_{\\text{ode}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg\" width=\"36\" height=\"18\" data-width=\"4.508\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 4.508ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u0430\u043a\u0438\u0445 \u0448\u0430\u0433\u043e\u0432 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0444\u0438\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u043f\u043e\u0445\u043e\u0436 \u043d\u0430 \u0434\u0430\u043d\u043d\u044b\u0435. \u0415\u0441\u043b\u0438 \u043d\u0443\u0436\u043d\u043e \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432, \u0442\u043e\u0442 \u0436\u0435 \u0446\u0438\u043a\u043b \u043e\u0431\u044b\u0447\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u043e \u0434\u043b\u044f \u0431\u0430\u0442\u0447\u0430 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0445 \u0448\u0443\u043c\u043e\u0432.<\/p>\n<ul>\n<li>\n<p>\u2699\ufe0f <strong>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c:<\/strong> \u0421\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e Flow Matching\u2019\u0430<\/p>\n<\/li>\n<li>\n<p><strong>\u0412\u0445\u043e\u0434:<\/strong> \u041e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\theta\" alt=\"u_\\theta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg\" width=\"18\" height=\"18\" data-width=\"2.232\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.232ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0448\u0430\u0433\u043e\u0432 \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"K_{\\text{ode}}\" alt=\"K_{\\text{ode}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg\" width=\"36\" height=\"18\" data-width=\"4.508\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 4.508ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab6\/ab6eb7c8ff11bc4ab01e33b9f5565478.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><strong>\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/strong> \u0421\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}\" alt=\"\\hat{x}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2a\/2a9\/2a95aaaf954c2187999c6357b04a58dd.svg\" width=\"12\" height=\"19\" data-width=\"1.294\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 1.294ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2a\/2a9\/2a95aaaf954c2187999c6357b04a58dd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2a\/2a9\/2a95aaaf954c2187999c6357b04a58dd.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0439 \u0448\u0443\u043c: <img decoding=\"async\" class=\"formula inline\" source=\"x \\sim \\mathcal{N}(0,I)\" alt=\"x \\sim \\mathcal{N}(0,I)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70d\/70dfe037182972a97a97c8ec0e187836.svg\" width=\"93\" height=\"19\" data-width=\"11.564\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 11.564ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70d\/70dfe037182972a97a97c8ec0e187836.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70d\/70dfe037182972a97a97c8ec0e187836.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0417\u0430\u0434\u0430\u0451\u043c \u0440\u0430\u0437\u043c\u0435\u0440 \u0448\u0430\u0433\u0430 \u043f\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"\\Delta t \\gets \\frac{1}{K_{\\text{ode}}}\" alt=\"\\Delta t \\gets \\frac{1}{K_{\\text{ode}}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd2\/bd21b1c99ee4ec4878ec67238abf4dc6.svg\" width=\"94\" height=\"40\" data-width=\"11.724\" data-height=\"4.945\" data-vertical-align=\"-1.907\" style=\"width: 11.724ex; height: 4.945ex; vertical-align: -1.907ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd2\/bd21b1c99ee4ec4878ec67238abf4dc6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd2\/bd21b1c99ee4ec4878ec67238abf4dc6.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><strong>\u0414\u043b\u044f<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"k = 0\" alt=\"k = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/88\/88c\/88ca2849b6983bdef7879ade5527dd3d.svg\" width=\"43\" height=\"14\" data-width=\"5.327\" data-height=\"1.756\" data-vertical-align=\"-0.186\" style=\"width: 5.327ex; height: 1.756ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/88\/88c\/88ca2849b6983bdef7879ade5527dd3d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/88\/88c\/88ca2849b6983bdef7879ade5527dd3d.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e <img decoding=\"async\" class=\"formula inline\" source=\"K_{\\text{ode}}-1\" alt=\"K_{\\text{ode}}-1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fd1\/fd1f2a02ccdbaa3e89429ca09976bc69.svg\" width=\"67\" height=\"18\" data-width=\"8.405\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 8.405ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fd1\/fd1f2a02ccdbaa3e89429ca09976bc69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fd1\/fd1f2a02ccdbaa3e89429ca09976bc69.svg 781w\" loading=\"lazy\" decode=\"async\"\/> <\/p>\n<ul>\n<li>\n<p>\u0422\u0435\u043a\u0443\u0449\u0435\u0435 \u0432\u0440\u0435\u043c\u044f: <img decoding=\"async\" class=\"formula inline\" source=\"t_k \\gets k\\Delta t\" alt=\"t_k \\gets k\\Delta t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30d\/30d7c7c4a9aa436dfee391da6aa5e6c8.svg\" width=\"74\" height=\"18\" data-width=\"9.237\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 9.237ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30d\/30d7c7c4a9aa436dfee391da6aa5e6c8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30d\/30d7c7c4a9aa436dfee391da6aa5e6c8.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u043c \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432 \u0442\u0435\u043a\u0443\u0449\u0435\u0439 \u0442\u043e\u0447\u043a\u0435: <img decoding=\"async\" class=\"formula inline\" source=\"v_k \\gets u_\\theta(x,t_k)\" alt=\"v_k \\gets u_\\theta(x,t_k)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e2\/e24\/e2475a11f4e0fbc8580a3eb88cae5cb8.svg\" width=\"110\" height=\"18\" data-width=\"13.768\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 13.768ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e2\/e24\/e2475a11f4e0fbc8580a3eb88cae5cb8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e2\/e24\/e2475a11f4e0fbc8580a3eb88cae5cb8.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0414\u0435\u043b\u0430\u0435\u043c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0439 \u0448\u0430\u0433 \u043f\u043e \u043f\u043e\u043b\u044e: <img decoding=\"async\" class=\"formula inline\" source=\"x \\gets x + \\Delta t \\cdot v_k\" alt=\"x \\gets x + \\Delta t \\cdot v_k\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acd\/acdb42ee78cb9de22e22565bd9f1986c.svg\" width=\"123\" height=\"18\" data-width=\"15.328\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 15.328ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acd\/acdb42ee78cb9de22e22565bd9f1986c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acd\/acdb42ee78cb9de22e22565bd9f1986c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x} \\gets x\" alt=\"\\hat{x} \\gets x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/67d\/67d6c49503c2936ba29faa4d2ba99b64.svg\" width=\"49\" height=\"19\" data-width=\"6.108\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 6.108ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/67d\/67d6c49503c2936ba29faa4d2ba99b64.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/67\/67d\/67d6c49503c2936ba29faa4d2ba99b64.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<p>\u0417\u0434\u0435\u0441\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0441\u0430\u043c\u044b\u0439 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043c\u0435\u0442\u043e\u0434 \u2014 \u043c\u0435\u0442\u043e\u0434 \u042d\u0439\u043b\u0435\u0440\u0430. \u041e\u043d \u0431\u0443\u043a\u0432\u0430\u043b\u044c\u043d\u043e \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u0435\u0442 \u043d\u0430\u0448\u0443 \u0438\u043d\u0442\u0443\u0438\u0446\u0438\u044e: \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043d\u0430 \u0442\u0435\u043a\u0443\u0449\u0443\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c, \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0439 \u0448\u0430\u0433 \u0432 \u044d\u0442\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438, \u0437\u0430\u0442\u0435\u043c \u0441\u043d\u043e\u0432\u0430 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043d\u0430 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0438 \u0441\u043d\u043e\u0432\u0430 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0448\u0430\u0433. \u0427\u0435\u043c \u0431\u043e\u043b\u044c\u0448\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"K\" alt=\"K\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg\" width=\"16\" height=\"12\" data-width=\"2.011\" data-height=\"1.545\" style=\"width: 2.011ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u0435\u043c \u0442\u043e\u0447\u043d\u0435\u0435 \u043c\u044b \u0441\u043b\u0435\u0434\u0443\u0435\u043c \u0432\u044b\u0443\u0447\u0435\u043d\u043d\u043e\u043c\u0443 \u043f\u043e\u043b\u044e, \u043d\u043e \u0442\u0435\u043c \u043c\u0435\u0434\u043b\u0435\u043d\u043d\u0435\u0435 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044f.<\/p>\n<p>\u0412 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u0441\u043a\u0440\u044b\u0442\u043e\u043c \u0431\u043b\u043e\u043a\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0432\u044b\u0432\u043e\u0434 Flow Matching\u2019\u0430 \u0447\u0435\u0440\u0435\u0437 \u043f\u0440\u043e\u0431\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0440\u0430\u0437\u0431\u043e\u0440 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438. \u042d\u0442\u043e \u043f\u043e\u0437\u0432\u043e\u043b\u0438\u0442 \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043e\u0442 \u0438\u043d\u0442\u0443\u0438\u0446\u0438\u0438 \u043a \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044e \u043c\u0435\u0442\u043e\u0434\u0430.<\/p>\n<details class=\"spoiler\">\n<summary>\u0424\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0432\u044b\u0432\u043e\u0434<\/summary>\n<div class=\"spoiler__content\">\n<p>\u0418\u0442\u0430\u043a, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0431\u043e\u043b\u0435\u0435 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u043e\u0431\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043f\u043e\u043a\u0430\u0436\u0435\u043c, \u043f\u043e\u0447\u0435\u043c\u0443 Flow Matching \u0443\u0447\u0438\u0442 \u0438\u043c\u0435\u043d\u043d\u043e \u043f\u043e\u043b\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^*(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ x_1 - x_0 \\mid x_t = x \\right],\" alt=\"u^*(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ x_1 - x_0 \\mid x_t = x \\right],\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1b2\/1b21bb0991918234c11ae2d228277bb0.svg\" width=\"354\" height=\"20\" data-width=\"44.261\" data-height=\"2.559\" data-vertical-align=\"-0.714\" style=\"width: 44.261ex; height: 2.559ex; vertical-align: -0.714ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1b2\/1b21bb0991918234c11ae2d228277bb0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1b2\/1b21bb0991918234c11ae2d228277bb0.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418 \u043f\u043e\u0447\u0435\u043c\u0443, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0434\u0432\u0438\u0433\u0430\u044f\u0441\u044c \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"u^*(x_t, t)\" alt=\"u^*(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fab\/fabd937d05e58aa0cac624c864a0be69.svg\" width=\"63\" height=\"18\" data-width=\"7.924\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.924ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fab\/fabd937d05e58aa0cac624c864a0be69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fab\/fabd937d05e58aa0cac624c864a0be69.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0442\u043e \u0436\u0435 \u0441\u0430\u043c\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u0430\u043a \u0435\u0441\u043b\u0438 \u0431\u044b \u043c\u044b \u043f\u0440\u043e\u0441\u0442\u043e \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u0435\u0433\u043e \u043a\u0430\u043a <img decoding=\"async\" class=\"formula inline\" source=\"x_t = (1-t)x_0 + t x_1\" alt=\"x_t = (1-t)x_0 + t x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5b\/5b5\/5b5b1567db59db5e87e1d8c73edd87bb.svg\" width=\"158\" height=\"18\" data-width=\"19.696\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 19.696ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5b\/5b5\/5b5b1567db59db5e87e1d8c73edd87bb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5b\/5b5\/5b5b1567db59db5e87e1d8c73edd87bb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_t = (1-t)x_0 + t x_1,\" alt=\"x_t = (1-t)x_0 + t x_1,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e0ada07fe4a3be4841ca9fa2983c9.svg\" width=\"163\" height=\"18\" data-width=\"20.325\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 20.325ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e0ada07fe4a3be4841ca9fa2983c9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e0ada07fe4a3be4841ca9fa2983c9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0413\u0434\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_0 \\sim \\mathcal{N}(0,I), \\qquad x_1 \\sim p_{\\text{data}}.\" alt=\"x_0 \\sim \\mathcal{N}(0,I), \\qquad x_1 \\sim p_{\\text{data}}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9c\/9c3\/9c39cae250288a30bd7950b7ce4b1800.svg\" width=\"228\" height=\"19\" data-width=\"28.448\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 28.448ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9c\/9c3\/9c39cae250288a30bd7950b7ce4b1800.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9c\/9c3\/9c39cae250288a30bd7950b7ce4b1800.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0414\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u043f\u0430\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"(x_0,x_1)\" alt=\"(x_0,x_1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg\" width=\"59\" height=\"18\" data-width=\"7.33\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.33ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432\u0434\u043e\u043b\u044c \u043f\u0440\u044f\u043c\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d x_t}{dt} = x_1 - x_0.\" alt=\"\\frac{d x_t}{dt} = x_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3bea659eb96ca1f8ee38dacdcfefa223.svg\" width=\"122\" height=\"37\" data-width=\"15.207\" data-height=\"4.676\" data-vertical-align=\"-1.773\" style=\"width: 15.207ex; height: 4.676ex; vertical-align: -1.773ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3bea659eb96ca1f8ee38dacdcfefa223.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3b\/3be\/3bea659eb96ca1f8ee38dacdcfefa223.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0443\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"p_t(x)\" alt=\"p_t(x)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd1\/bd17ac345974b4fb9bb73d3cefa6878e.svg\" width=\"40\" height=\"18\" data-width=\"4.958\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 4.958ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd1\/bd17ac345974b4fb9bb73d3cefa6878e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bd\/bd1\/bd17ac345974b4fb9bb73d3cefa6878e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041c\u044b \u0445\u043e\u0442\u0438\u043c \u043f\u043e\u043d\u044f\u0442\u044c, \u043a\u0430\u043a \u043e\u043d\u0430 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0441\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0435\u043c.<\/p>\n<p>\u0412\u043e\u0437\u044c\u043c\u0451\u043c 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https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0d198aafe69f3d39c23049f80a993d3.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e\u0433\u0434\u0430 \u0434\u043b\u044f \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\int \\varphi(x)\\,p_t(x)\\,dx.\" alt=\"\\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\int \\varphi(x)\\,p_t(x)\\,dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/93\/939\/939387fb0e321dcc9ac7383688eb6976.svg\" width=\"336\" height=\"40\" data-width=\"42.046\" data-height=\"5.027\" data-vertical-align=\"-1.948\" style=\"width: 42.046ex; height: 5.027ex; vertical-align: -1.948ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/93\/939\/939387fb0e321dcc9ac7383688eb6976.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/93\/939\/939387fb0e321dcc9ac7383688eb6976.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0440\u043e\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c \u044d\u0442\u043e \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435 \u043f\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\frac{d}{dt}\\varphi(x_t) \\right].\" alt=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\frac{d}{dt}\\varphi(x_t) \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f1c\/f1c9b3318fa5b30d3c9a8d82c4d1f83e.svg\" width=\"457\" height=\"43\" data-width=\"57.093\" data-height=\"5.428\" data-vertical-align=\"-2.148\" style=\"width: 57.093ex; height: 5.428ex; vertical-align: -2.148ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f1c\/f1c9b3318fa5b30d3c9a8d82c4d1f83e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f1c\/f1c9b3318fa5b30d3c9a8d82c4d1f83e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0443 \u0446\u0435\u043f\u043e\u0447\u043a\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt}\\varphi(x_t) = \\nabla \\varphi(x_t)\\cdot \\frac{d x_t}{dt} = \\nabla \\varphi(x_t)\\cdot (x_1-x_0).\" alt=\"\\frac{d}{dt}\\varphi(x_t) = \\nabla \\varphi(x_t)\\cdot \\frac{d x_t}{dt} = \\nabla \\varphi(x_t)\\cdot (x_1-x_0).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e7\/3e79c05c0dddeb9cc72ffbdb4b4e3ff4.svg\" width=\"367\" height=\"37\" data-width=\"45.909\" data-height=\"4.676\" data-vertical-align=\"-1.773\" style=\"width: 45.909ex; height: 4.676ex; vertical-align: -1.773ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e7\/3e79c05c0dddeb9cc72ffbdb4b4e3ff4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e7\/3e79c05c0dddeb9cc72ffbdb4b4e3ff4.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u043d\u0430\u0447\u0438\u0442:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\nabla \\varphi(x_t)\\cdot (x_1-x_0) \\right].\" alt=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\nabla \\varphi(x_t)\\cdot (x_1-x_0) \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/77\/77a\/77abfc0a5194e229608be86e7336d581.svg\" width=\"525\" height=\"37\" data-width=\"65.582\" data-height=\"4.676\" data-vertical-align=\"-1.773\" style=\"width: 65.582ex; height: 4.676ex; vertical-align: -1.773ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/77\/77a\/77abfc0a5194e229608be86e7336d581.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/77\/77a\/77abfc0a5194e229608be86e7336d581.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435 \u043f\u043e \u0442\u0435\u043a\u0443\u0449\u0435\u0439 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\nabla \\varphi(x_t)\\cdot (x_1-x_0) \\right] = \\mathbb{E}_{x_t} \\left[ \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\nabla \\varphi(x_t)\\cdot (x_1-x_0) \\mid x_t \\right] \\right].\" alt=\"\\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\nabla \\varphi(x_t)\\cdot (x_1-x_0) \\right] = \\mathbb{E}_{x_t} \\left[ \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\nabla \\varphi(x_t)\\cdot (x_1-x_0) \\mid x_t \\right] \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/47\/479\/47949b9d07ce214b3de6eb4bb1b5c6ec.svg\" width=\"677\" height=\"22\" data-width=\"84.564\" data-height=\"2.784\" data-vertical-align=\"-0.826\" style=\"width: 84.564ex; height: 2.784ex; vertical-align: -0.826ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/47\/479\/47949b9d07ce214b3de6eb4bb1b5c6ec.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/47\/479\/47949b9d07ce214b3de6eb4bb1b5c6ec.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a \u043a\u0430\u043a <img decoding=\"async\" class=\"formula inline\" source=\"\\nabla\\varphi(x_t)\" alt=\"\\nabla\\varphi(x_t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7f\/7fc\/7fcc0e05a7bf6983973dcfc236d6f99d.svg\" width=\"57\" height=\"18\" data-width=\"7.184\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.184ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7f\/7fc\/7fcc0e05a7bf6983973dcfc236d6f99d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7f\/7fc\/7fcc0e05a7bf6983973dcfc236d6f99d.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"x_t\" alt=\"x_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg\" width=\"16\" height=\"12\" data-width=\"2.059\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.059ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cf\/cf7\/cf7ee950cf61a6003c0ec4af7971d8a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0435\u0451 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u043d\u0435\u0441\u0442\u0438 \u0438\u0437 \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0435\u0433\u043e \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0433\u043e \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u044f:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\nabla \\varphi(x_t)\\cdot (x_1-x_0) \\mid x_t \\right] = \\nabla \\varphi(x_t) \\cdot \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ x_1-x_0 \\mid x_t \\right].\" alt=\"\\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\nabla \\varphi(x_t)\\cdot (x_1-x_0) \\mid x_t \\right] = \\nabla \\varphi(x_t) \\cdot \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ x_1-x_0 \\mid x_t \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0e\/0e4\/0e49791cf4026c92538d0f266c744815.svg\" width=\"651\" height=\"20\" data-width=\"81.332\" data-height=\"2.559\" data-vertical-align=\"-0.714\" style=\"width: 81.332ex; height: 2.559ex; vertical-align: -0.714ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0e\/0e4\/0e49791cf4026c92538d0f266c744815.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0e\/0e4\/0e49791cf4026c92538d0f266c744815.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412\u0432\u0435\u0434\u0451\u043c \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^*(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ x_1-x_0 \\mid x_t=x \\right].\" alt=\"u^*(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ x_1-x_0 \\mid x_t=x \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2f\/2ff\/2ff674d7f41e6199debdbb1aabe2fa97.svg\" width=\"354\" height=\"20\" data-width=\"44.261\" data-height=\"2.559\" data-vertical-align=\"-0.714\" style=\"width: 44.261ex; height: 2.559ex; vertical-align: -0.714ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2f\/2ff\/2ff674d7f41e6199debdbb1aabe2fa97.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2f\/2ff\/2ff674d7f41e6199debdbb1aabe2fa97.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e\u0433\u0434\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\mathbb{E}_{x_t} \\left[ \\nabla \\varphi(x_t)\\cdot u^*(x_t,t) \\right].\" alt=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\mathbb{E}_{x_t} \\left[ \\nabla \\varphi(x_t)\\cdot u^*(x_t,t) \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1d6\/1d615979528cc012ba5bee70d65d36c7.svg\" width=\"411\" height=\"37\" data-width=\"51.335\" data-height=\"4.676\" data-vertical-align=\"-1.773\" style=\"width: 51.335ex; height: 4.676ex; vertical-align: -1.773ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1d6\/1d615979528cc012ba5bee70d65d36c7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1d6\/1d615979528cc012ba5bee70d65d36c7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u043c \u043a \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u0443 \u043f\u043e \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"p_t\" alt=\"p_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg\" width=\"15\" height=\"12\" data-width=\"1.903\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 1.903ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\int \\nabla \\varphi(x)\\cdot u^*(x,t)\\,p_t(x)\\,dx.\" alt=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\int \\nabla \\varphi(x)\\cdot u^*(x,t)\\,p_t(x)\\,dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/392\/3925f19b818b4719b2c3e5f35769a937.svg\" width=\"446\" height=\"40\" data-width=\"55.713\" data-height=\"5.048\" data-vertical-align=\"-1.958\" style=\"width: 55.713ex; height: 5.048ex; vertical-align: -1.958ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/392\/3925f19b818b4719b2c3e5f35769a937.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/392\/3925f19b818b4719b2c3e5f35769a937.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u043e\u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u043c \u043f\u043e \u0447\u0430\u0441\u0442\u044f\u043c. \u0422\u0430\u043a \u043a\u0430\u043a <img decoding=\"async\" class=\"formula inline\" source=\"\\varphi\" alt=\"\\varphi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg\" width=\"12\" height=\"18\" data-width=\"1.48\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.48ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043c\u0435\u0435\u0442 \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u044b\u0439 \u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c, \u0433\u0440\u0430\u043d\u0438\u0447\u043d\u044b\u0435 \u0447\u043b\u0435\u043d\u044b \u0438\u0441\u0447\u0435\u0437\u0430\u044e\u0442 (\u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u043e\u043d\u0438 \u0440\u0430\u0432\u043d\u044b 0):<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\int \\nabla \\varphi(x)\\cdot u^*(x,t)\\,p_t(x)\\,dx = - \\int \\varphi(x)\\, \\nabla\\cdot \\left( p_t(x)u^*(x,t) \\right) dx.\" alt=\"\\int \\nabla \\varphi(x)\\cdot u^*(x,t)\\,p_t(x)\\,dx = - \\int \\varphi(x)\\, \\nabla\\cdot \\left( p_t(x)u^*(x,t) \\right) dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fa2\/fa25ba5523036bfd37bb4ef23b1b338d.svg\" width=\"472\" height=\"40\" data-width=\"58.983\" data-height=\"5.027\" data-vertical-align=\"-1.948\" style=\"width: 58.983ex; height: 5.027ex; vertical-align: -1.948ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fa2\/fa25ba5523036bfd37bb4ef23b1b338d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fa2\/fa25ba5523036bfd37bb4ef23b1b338d.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\frac{d}{dt} \\int \\varphi(x)p_t(x)\\,dx = \\int \\varphi(x) \\frac{\\partial p_t(x)}{\\partial t} dx.\" alt=\"\\frac{d}{dt} \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I),\\,x_1\\sim p_{\\text{data}}} \\left[ \\varphi(x_t) \\right] = \\frac{d}{dt} \\int \\varphi(x)p_t(x)\\,dx = \\int \\varphi(x) \\frac{\\partial p_t(x)}{\\partial t} dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cd\/cd3\/cd38c5c364f6ed9ecc8ff84ffa7a0d41.svg\" width=\"542\" height=\"42\" data-width=\"67.791\" data-height=\"5.251\" data-vertical-align=\"-2.06\" style=\"width: 67.791ex; height: 5.251ex; vertical-align: -2.06ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cd\/cd3\/cd38c5c364f6ed9ecc8ff84ffa7a0d41.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cd\/cd3\/cd38c5c364f6ed9ecc8ff84ffa7a0d41.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u043d\u0430\u0447\u0438\u0442:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\int \\varphi(x) \\frac{\\partial p_t(x)}{\\partial t} dx = - \\int \\varphi(x) \\nabla\\cdot \\left( p_t(x)u^*(x,t) \\right) dx.\" alt=\"\\int \\varphi(x) \\frac{\\partial p_t(x)}{\\partial t} dx = - \\int \\varphi(x) \\nabla\\cdot \\left( p_t(x)u^*(x,t) \\right) dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/52\/52d\/52dc80fa9c41fba741eb9aabae6c46c2.svg\" width=\"396\" height=\"42\" data-width=\"49.447\" data-height=\"5.251\" data-vertical-align=\"-2.06\" style=\"width: 49.447ex; height: 5.251ex; vertical-align: -2.06ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/52\/52d\/52dc80fa9c41fba741eb9aabae6c46c2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/52\/52d\/52dc80fa9c41fba741eb9aabae6c46c2.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u043b\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\int \\varphi(x) \\left[ \\frac{\\partial p_t(x)}{\\partial t} + \\nabla\\cdot \\left( p_t(x)u^*(x,t) \\right) \\right] dx = 0.\" alt=\"\\int \\varphi(x) \\left[ \\frac{\\partial p_t(x)}{\\partial t} + \\nabla\\cdot \\left( p_t(x)u^*(x,t) \\right) \\right] dx = 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/83\/836\/836feda34b460838c2a81910bf675d58.svg\" width=\"356\" height=\"44\" data-width=\"44.456\" data-height=\"5.451\" data-vertical-align=\"-2.16\" style=\"width: 44.456ex; height: 5.451ex; vertical-align: -2.16ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/83\/836\/836feda34b460838c2a81910bf675d58.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/83\/836\/836feda34b460838c2a81910bf675d58.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u042d\u0442\u043e \u0432\u0435\u0440\u043d\u043e \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0439 \u043f\u0440\u043e\u0431\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\varphi\" alt=\"\\varphi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg\" width=\"12\" height=\"18\" data-width=\"1.48\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.48ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c <strong>\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438<\/strong> \u0434\u043b\u044f \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"p_t\" alt=\"p_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg\" width=\"15\" height=\"12\" data-width=\"1.903\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 1.903ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial p_t}{\\partial t} + \\nabla\\cdot \\left( p_t u^* \\right) = 0.\" alt=\"\\frac{\\partial p_t}{\\partial t} + \\nabla\\cdot \\left( p_t u^* \\right) = 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e2\/e25\/e25fffc2901fd46a2f1958ce3ca44e27.svg\" width=\"169\" height=\"38\" data-width=\"21.187\" data-height=\"4.749\" data-vertical-align=\"-1.809\" style=\"width: 21.187ex; height: 4.749ex; vertical-align: -1.809ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e2\/e25\/e25fffc2901fd46a2f1958ce3ca44e27.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e2\/e25\/e25fffc2901fd46a2f1958ce3ca44e27.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u0442\u0430\u043a, \u043c\u044b \u043f\u043e\u043a\u0430\u0437\u0430\u043b\u0438 \u2014 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"p_t\" alt=\"p_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg\" width=\"15\" height=\"12\" data-width=\"1.903\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 1.903ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0437 \u043f\u0440\u044f\u043c\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_t = (1-t)x_0 + t x_1,\" alt=\"x_t = (1-t)x_0 + t x_1,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e0ada07fe4a3be4841ca9fa2983c9.svg\" width=\"163\" height=\"18\" data-width=\"20.325\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 20.325ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e0ada07fe4a3be4841ca9fa2983c9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e0ada07fe4a3be4841ca9fa2983c9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0423\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 \u0441 \u043f\u043e\u043b\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u^*(x,t)\" alt=\"u^*(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg\" width=\"57\" height=\"18\" data-width=\"7.159\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.159ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u041d\u043e \u043f\u043e\u0447\u0435\u043c\u0443 \u043c\u043e\u0436\u043d\u043e \u0434\u0432\u0438\u0433\u0430\u0442\u044c\u0441\u044f \u043f\u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c\u0443 \u043f\u043e\u043b\u044e?<\/p>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u043e\u0432\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438. \u0412\u043e\u0437\u044c\u043c\u0451\u043c \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\tilde{x}_0 \\sim \\mathcal{N}(0,I)\" alt=\"\\tilde{x}_0 \\sim \\mathcal{N}(0,I)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a7\/a78\/a789370788b24636f3a420803b4c39e6.svg\" width=\"100\" height=\"19\" data-width=\"12.552\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.552ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a7\/a78\/a789370788b24636f3a420803b4c39e6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a7\/a78\/a789370788b24636f3a420803b4c39e6.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418 \u0431\u0443\u0434\u0435\u043c \u0434\u0432\u0438\u0433\u0430\u0442\u044c \u0435\u0451 \u043f\u043e ODE:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d \\tilde{x}_t}{dt} = u^*(\\tilde{x}_t,t).\" alt=\"\\frac{d \\tilde{x}_t}{dt} = u^*(\\tilde{x}_t,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8c5\/8c55a1156c0c809a636cf4092c367ebc.svg\" width=\"126\" height=\"38\" data-width=\"15.802\" data-height=\"4.803\" data-vertical-align=\"-1.836\" style=\"width: 15.802ex; height: 4.803ex; vertical-align: -1.836ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8c5\/8c55a1156c0c809a636cf4092c367ebc.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8c5\/8c55a1156c0c809a636cf4092c367ebc.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0443\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"q_t(x)\" alt=\"q_t(x)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea3\/ea30b8293e18c58fa7a6a9b64b3e1356.svg\" width=\"39\" height=\"18\" data-width=\"4.829\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 4.829ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea3\/ea30b8293e18c58fa7a6a9b64b3e1356.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea3\/ea30b8293e18c58fa7a6a9b64b3e1356.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b <img decoding=\"async\" class=\"formula inline\" source=\"\\tilde{x}_t\" alt=\"\\tilde{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4c\/f4c20dd3ec59de4e318cdbea4deb8410.svg\" width=\"16\" height=\"18\" data-width=\"2.059\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.059ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4c\/f4c20dd3ec59de4e318cdbea4deb8410.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4c\/f4c20dd3ec59de4e318cdbea4deb8410.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e \u043f\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \u044d\u0442\u0430 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"q_t\" alt=\"q_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg\" width=\"14\" height=\"12\" data-width=\"1.774\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 1.774ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u043e\u0436\u0435 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438.<\/p>\n<p>\u0421\u043d\u043e\u0432\u0430 \u0432\u043e\u0437\u044c\u043c\u0435\u043c \u0433\u043b\u0430\u0434\u043a\u0443\u044e \u043f\u0440\u043e\u0431\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e <img decoding=\"async\" class=\"formula inline\" source=\"\\varphi\" alt=\"\\varphi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg\" width=\"12\" height=\"18\" data-width=\"1.48\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.48ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\varphi(\\tilde{x}_t) \\right] = \\int \\varphi(x)q_t(x)\\,dx.\" alt=\"\\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\varphi(\\tilde{x}_t) \\right] = \\int \\varphi(x)q_t(x)\\,dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/733\/733238cae3312144526bce09530edcb9.svg\" width=\"278\" height=\"40\" data-width=\"34.721\" data-height=\"5.027\" data-vertical-align=\"-1.948\" style=\"width: 34.721ex; height: 5.027ex; vertical-align: -1.948ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/733\/733238cae3312144526bce09530edcb9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/733\/733238cae3312144526bce09530edcb9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0440\u043e\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c \u044d\u0442\u043e \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435 \u043f\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt} \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\varphi(\\tilde{x}_t) \\right] = \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\frac{d}{dt}\\varphi(\\tilde{x}_t) \\right].\" alt=\"\\frac{d}{dt} \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\varphi(\\tilde{x}_t) \\right] = \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\frac{d}{dt}\\varphi(\\tilde{x}_t) \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/92f\/92f774f35c99b962a7ecfbf8e35b3121.svg\" width=\"348\" height=\"43\" data-width=\"43.457\" data-height=\"5.428\" data-vertical-align=\"-2.148\" style=\"width: 43.457ex; height: 5.428ex; vertical-align: -2.148ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/92f\/92f774f35c99b962a7ecfbf8e35b3121.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/92f\/92f774f35c99b962a7ecfbf8e35b3121.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0443 \u0446\u0435\u043f\u043e\u0447\u043a\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt}\\varphi(\\tilde{x}_t) = \\nabla\\varphi(\\tilde{x}_t)\\cdot \\frac{d \\tilde{x}_t}{dt}.\" alt=\"\\frac{d}{dt}\\varphi(\\tilde{x}_t) = \\nabla\\varphi(\\tilde{x}_t)\\cdot \\frac{d \\tilde{x}_t}{dt}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/73e\/73ea1ab8be6c3491332abeda8456287f.svg\" width=\"200\" height=\"38\" data-width=\"24.984\" data-height=\"4.803\" data-vertical-align=\"-1.836\" style=\"width: 24.984ex; height: 4.803ex; vertical-align: -1.836ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/73e\/73ea1ab8be6c3491332abeda8456287f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/73\/73e\/73ea1ab8be6c3491332abeda8456287f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a \u043a\u0430\u043a <img decoding=\"async\" class=\"formula inline\" source=\"\\tilde{x}_t\" alt=\"\\tilde{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4c\/f4c20dd3ec59de4e318cdbea4deb8410.svg\" width=\"16\" height=\"18\" data-width=\"2.059\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.059ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4c\/f4c20dd3ec59de4e318cdbea4deb8410.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4c\/f4c20dd3ec59de4e318cdbea4deb8410.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u0432\u0438\u0436\u0435\u0442\u0441\u044f \u043f\u043e ODE:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d \\tilde{x}_t}{dt} = u^*(\\tilde{x}_t,t),\" alt=\"\\frac{d \\tilde{x}_t}{dt} = u^*(\\tilde{x}_t,t),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c42\/c420e641bf7eaf86433a2c4aa67bcb1b.svg\" width=\"126\" height=\"38\" data-width=\"15.802\" data-height=\"4.803\" data-vertical-align=\"-1.836\" style=\"width: 15.802ex; height: 4.803ex; vertical-align: -1.836ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c42\/c420e641bf7eaf86433a2c4aa67bcb1b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c42\/c420e641bf7eaf86433a2c4aa67bcb1b.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt} \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\varphi(\\tilde{x}_t) \\right] = \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\nabla\\varphi(\\tilde{x}_t)\\cdot u^*(\\tilde{x}_t,t) \\right].\" alt=\"\\frac{d}{dt} \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\varphi(\\tilde{x}_t) \\right] = \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\nabla\\varphi(\\tilde{x}_t)\\cdot u^*(\\tilde{x}_t,t) \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/27\/27a\/27a4af138f003c1f6405769de50a5d25.svg\" width=\"406\" height=\"37\" data-width=\"50.78\" data-height=\"4.676\" data-vertical-align=\"-1.773\" style=\"width: 50.78ex; height: 4.676ex; vertical-align: -1.773ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/27\/27a\/27a4af138f003c1f6405769de50a5d25.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/27\/27a\/27a4af138f003c1f6405769de50a5d25.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0435\u0440\u0435\u043f\u0438\u0448\u0435\u043c \u044d\u0442\u043e \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435 \u043a\u0430\u043a \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b \u043f\u043e \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"q_t\" alt=\"q_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg\" width=\"14\" height=\"12\" data-width=\"1.774\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 1.774ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\nabla\\varphi(\\tilde{x}_t)\\cdot u^*(\\tilde{x}_t,t) \\right] = \\int \\nabla\\varphi(x)\\cdot u^*(x,t)q_t(x)\\,dx.\" alt=\"\\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\nabla\\varphi(\\tilde{x}_t)\\cdot u^*(\\tilde{x}_t,t) \\right] = \\int \\nabla\\varphi(x)\\cdot u^*(x,t)q_t(x)\\,dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/76\/766\/766fd2f03bf5fb214b2d7d477674b11f.svg\" width=\"455\" height=\"40\" data-width=\"56.842\" data-height=\"5.027\" data-vertical-align=\"-1.948\" style=\"width: 56.842ex; height: 5.027ex; vertical-align: -1.948ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/76\/766\/766fd2f03bf5fb214b2d7d477674b11f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/76\/766\/766fd2f03bf5fb214b2d7d477674b11f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u043c \u043f\u043e \u0447\u0430\u0441\u0442\u044f\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\int \\nabla\\varphi(x)\\cdot u^*(x,t)q_t(x)\\,dx = - \\int \\varphi(x) \\nabla\\cdot \\left( q_t(x)u^*(x,t) \\right) dx.\" alt=\"\\int \\nabla\\varphi(x)\\cdot u^*(x,t)q_t(x)\\,dx = - \\int \\varphi(x) \\nabla\\cdot \\left( q_t(x)u^*(x,t) \\right) dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/24c\/24c50e47da4fe14e07cdee7c032ea4ff.svg\" width=\"464\" height=\"40\" data-width=\"57.969\" data-height=\"5.027\" data-vertical-align=\"-1.948\" style=\"width: 57.969ex; height: 5.027ex; vertical-align: -1.948ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/24c\/24c50e47da4fe14e07cdee7c032ea4ff.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/24c\/24c50e47da4fe14e07cdee7c032ea4ff.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d}{dt} \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\varphi(\\tilde{x}_t) \\right] = \\frac{d}{dt} \\int \\varphi(x)q_t(x)\\,dx = \\int \\varphi(x) \\frac{\\partial q_t(x)}{\\partial t} dx.\" alt=\"\\frac{d}{dt} \\mathbb{E}_{\\tilde{x}_0\\sim\\mathcal{N}(0,I)} \\left[ \\varphi(\\tilde{x}_t) \\right] = \\frac{d}{dt} \\int \\varphi(x)q_t(x)\\,dx = \\int \\varphi(x) \\frac{\\partial q_t(x)}{\\partial t} dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5a\/5ae\/5ae17402dd52cdd73e35f6799bb7f0aa.svg\" width=\"486\" height=\"42\" data-width=\"60.714\" data-height=\"5.251\" data-vertical-align=\"-2.06\" style=\"width: 60.714ex; height: 5.251ex; vertical-align: -2.06ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5a\/5ae\/5ae17402dd52cdd73e35f6799bb7f0aa.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5a\/5ae\/5ae17402dd52cdd73e35f6799bb7f0aa.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u043d\u0430\u0447\u0438\u0442:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\int \\varphi(x) \\frac{\\partial q_t(x)}{\\partial t} dx = - \\int \\varphi(x) \\nabla\\cdot \\left( q_t(x)u^*(x,t) \\right) dx.\" alt=\"\\int \\varphi(x) \\frac{\\partial q_t(x)}{\\partial t} dx = - \\int \\varphi(x) \\nabla\\cdot \\left( q_t(x)u^*(x,t) \\right) dx.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/ff\/ffe\/ffe8f89c98f43e06f0bf4b8c3ee4312e.svg\" width=\"394\" height=\"42\" data-width=\"49.189\" data-height=\"5.251\" data-vertical-align=\"-2.06\" style=\"width: 49.189ex; height: 5.251ex; vertical-align: -2.06ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/ff\/ffe\/ffe8f89c98f43e06f0bf4b8c3ee4312e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/ff\/ffe\/ffe8f89c98f43e06f0bf4b8c3ee4312e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u043b\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\int \\varphi(x) \\left[ \\frac{\\partial q_t(x)}{\\partial t} + \\nabla\\cdot \\left( q_t(x)u^*(x,t) \\right) \\right] dx = 0.\" alt=\"\\int \\varphi(x) \\left[ \\frac{\\partial q_t(x)}{\\partial t} + \\nabla\\cdot \\left( q_t(x)u^*(x,t) \\right) \\right] dx = 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/04\/047\/04778ac9d58cd4615f186c7389d8f18d.svg\" width=\"354\" height=\"44\" data-width=\"44.198\" data-height=\"5.451\" data-vertical-align=\"-2.16\" style=\"width: 44.198ex; height: 5.451ex; vertical-align: -2.16ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/04\/047\/04778ac9d58cd4615f186c7389d8f18d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/04\/047\/04778ac9d58cd4615f186c7389d8f18d.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a \u043a\u0430\u043a \u044d\u0442\u043e \u0432\u0435\u0440\u043d\u043e \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0439 \u043f\u0440\u043e\u0431\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\varphi\" alt=\"\\varphi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg\" width=\"12\" height=\"18\" data-width=\"1.48\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.48ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 \u0434\u043b\u044f \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"q_t\" alt=\"q_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg\" width=\"14\" height=\"12\" data-width=\"1.774\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 1.774ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/db\/db0\/db038f01db1d6ee8dea5f25727619cc1.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial q_t}{\\partial t} + \\nabla\\cdot \\left( q_t u^* \\right) = 0.\" alt=\"\\frac{\\partial q_t}{\\partial t} + \\nabla\\cdot \\left( q_t u^* \\right) = 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/17\/172\/172d64a836ae2bba74d2bd45a5de393b.svg\" width=\"167\" height=\"38\" data-width=\"20.929\" data-height=\"4.749\" data-vertical-align=\"-1.809\" style=\"width: 20.929ex; height: 4.749ex; vertical-align: -1.809ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/17\/172\/172d64a836ae2bba74d2bd45a5de393b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/17\/172\/172d64a836ae2bba74d2bd45a5de393b.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0441\u0440\u0430\u0432\u043d\u0438\u043c \u0434\u0432\u0430 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430. \u0414\u043b\u044f \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0445 \u043f\u0440\u044f\u043c\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial p_t}{\\partial t} + \\nabla\\cdot \\left( p_t u^* \\right) = 0, \\qquad p_0=\\mathcal{N}(0,I).\" alt=\"\\frac{\\partial p_t}{\\partial t} + \\nabla\\cdot \\left( p_t u^* \\right) = 0, \\qquad p_0=\\mathcal{N}(0,I).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a7\/a71\/a71ab6b9aa907789b51ab76ce8e288fa.svg\" width=\"313\" height=\"38\" data-width=\"39.113\" data-height=\"4.749\" data-vertical-align=\"-1.809\" style=\"width: 39.113ex; height: 4.749ex; vertical-align: -1.809ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a7\/a71\/a71ab6b9aa907789b51ab76ce8e288fa.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a7\/a71\/a71ab6b9aa907789b51ab76ce8e288fa.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0410 \u0434\u043b\u044f \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u043f\u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c\u0443 \u043f\u043e\u043b\u044e:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial q_t}{\\partial t} + \\nabla\\cdot \\left( q_t u^* \\right) = 0, \\qquad q_0=\\mathcal{N}(0,I).\" alt=\"\\frac{\\partial q_t}{\\partial t} + \\nabla\\cdot \\left( q_t u^* \\right) = 0, \\qquad q_0=\\mathcal{N}(0,I).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bb\/bb3\/bb3a317c8e9d494247f879cdab21041a.svg\" width=\"310\" height=\"38\" data-width=\"38.726\" data-height=\"4.749\" data-vertical-align=\"-1.809\" style=\"width: 38.726ex; height: 4.749ex; vertical-align: -1.809ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bb\/bb3\/bb3a317c8e9d494247f879cdab21041a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bb\/bb3\/bb3a317c8e9d494247f879cdab21041a.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u042d\u0442\u043e \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u043c \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u0435\u043c. \u041f\u0440\u0438 \u044d\u0442\u043e\u043c, \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u044f\u0432\u043d\u043e \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\frac{\\partial p_t}{\\partial t}\" alt=\"\\frac{\\partial p_t}{\\partial t}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41d\/41dd5998608f9a1e8e83af03dd388a63.svg\" width=\"33\" height=\"38\" data-width=\"4.179\" data-height=\"4.749\" data-vertical-align=\"-1.809\" style=\"width: 4.179ex; height: 4.749ex; vertical-align: -1.809ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41d\/41dd5998608f9a1e8e83af03dd388a63.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41d\/41dd5998608f9a1e8e83af03dd388a63.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e \u0442\u0435\u043a\u0443\u0449\u0438\u043c <img decoding=\"async\" class=\"formula inline\" source=\"p_t\" alt=\"p_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg\" width=\"15\" height=\"12\" data-width=\"1.903\" data-height=\"1.439\" data-vertical-align=\"-0.439\" style=\"width: 1.903ex; height: 1.439ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/01\/011\/011f9f40084dbe619093c6799fd364ca.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0417\u043d\u0430\u0447\u0438\u0442, \u0435\u0441\u043b\u0438 \u0435\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0442\u043e:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"q_t = p_t\" alt=\"q_t = p_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1bf\/1bfd75999c462c9095fe37910fc4c1e9.svg\" width=\"54\" height=\"14\" data-width=\"6.695\" data-height=\"1.758\" data-vertical-align=\"-0.439\" style=\"width: 6.695ex; height: 1.758ex; vertical-align: -0.439ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1bf\/1bfd75999c462c9095fe37910fc4c1e9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1bf\/1bfd75999c462c9095fe37910fc4c1e9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0434\u043b\u044f \u0432\u0441\u0435\u0445 <img decoding=\"async\" class=\"formula inline\" source=\"t\\in[0,1]\" alt=\"t\\in[0,1]\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/22\/22b\/22bafd6a4d2255a6c8b96ac73b92ea79.svg\" width=\"65\" height=\"18\" data-width=\"8.109\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 8.109ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/22\/22b\/22bafd6a4d2255a6c8b96ac73b92ea79.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/22\/22b\/22bafd6a4d2255a6c8b96ac73b92ea79.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<details class=\"spoiler\">\n<summary>\u0417\u0430\u0447\u0435\u043c \u043d\u0443\u0436\u043d\u0430 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/summary>\n<div class=\"spoiler__content\">\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"\\frac{dx}{dt}=2\\sqrt{|x|}\" alt=\"\\frac{dx}{dt}=2\\sqrt{|x|}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7a2\/7a2e8aa51192e2ccba674268dcee497a.svg\" width=\"100\" height=\"37\" data-width=\"12.474\" data-height=\"4.676\" data-vertical-align=\"-1.773\" style=\"width: 12.474ex; height: 4.676ex; vertical-align: -1.773ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7a2\/7a2e8aa51192e2ccba674268dcee497a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7a2\/7a2e8aa51192e2ccba674268dcee497a.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0418\u0437 \u0442\u043e\u0447\u043a\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x(0)=0\" alt=\"x(0)=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8da\/8da03aa5f2ca4d36d812595c5f45c31c.svg\" width=\"67\" height=\"18\" data-width=\"8.334\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 8.334ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8da\/8da03aa5f2ca4d36d812595c5f45c31c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8da\/8da03aa5f2ca4d36d812595c5f45c31c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0440\u0430\u0437\u043d\u044b\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f. \u041c\u043e\u0436\u043d\u043e \u043d\u0430\u0432\u0441\u0435\u0433\u0434\u0430 \u043e\u0441\u0442\u0430\u0442\u044c\u0441\u044f \u0432 \u043d\u0443\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x(t)=0\" alt=\"x(t)=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9a\/9a2\/9a24cbc4deed6e45b7ba770dec39fc17.svg\" width=\"64\" height=\"18\" data-width=\"8.019\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 8.019ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9a\/9a2\/9a24cbc4deed6e45b7ba770dec39fc17.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9a\/9a2\/9a24cbc4deed6e45b7ba770dec39fc17.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0447\u0430\u0442\u044c \u0434\u0432\u0438\u0433\u0430\u0442\u044c\u0441\u044f <img decoding=\"async\" class=\"formula inline\" source=\"x(t)=t^2\" alt=\"x(t)=t^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/71f\/71f4c78b4f4874a45e1e5a7a3d2d8560.svg\" width=\"70\" height=\"21\" data-width=\"8.693\" data-height=\"2.565\" data-vertical-align=\"-0.566\" style=\"width: 8.693ex; height: 2.565ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/71f\/71f4c78b4f4874a45e1e5a7a3d2d8560.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/71f\/71f4c78b4f4874a45e1e5a7a3d2d8560.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e, \u043c\u043e\u0436\u043d\u043e \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0441\u0442\u043e\u044f\u0442\u044c, \u0430 \u0437\u0430\u0442\u0435\u043c \u043d\u0430\u0447\u0430\u0442\u044c \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435 <\/p>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"x(t)= \\begin{cases} 0, &amp; 0 \\le t\\le \\tau,\\\\ (t-\\tau)^2, &amp; t&gt;\\tau. \\end{cases}, \\tau \\ge 0\" alt=\"x(t)= \\begin{cases} 0, &amp; 0 \\le t\\le \\tau,\\\\ (t-\\tau)^2, &amp; t&gt;\\tau. \\end{cases}, \\tau \\ge 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/64\/64e\/64e4281a1f5d3401a4263a1f0e7784ee.svg\" width=\"281\" height=\"43\" data-width=\"35.081\" data-height=\"5.428\" data-vertical-align=\"-2.148\" style=\"width: 35.081ex; height: 5.428ex; vertical-align: -2.148ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/64\/64e\/64e4281a1f5d3401a4263a1f0e7784ee.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/64\/64e\/64e4281a1f5d3401a4263a1f0e7784ee.svg 781w\" loading=\"lazy\" decode=\"async\"\/> <\/p>\n<p>\u0412\u0441\u0435 \u044d\u0442\u0438 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u043d\u0443 \u0438 \u0442\u0443 \u0436\u0435 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x(0)=0\" alt=\"x(0)=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8da\/8da03aa5f2ca4d36d812595c5f45c31c.svg\" width=\"67\" height=\"18\" data-width=\"8.334\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 8.334ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8da\/8da03aa5f2ca4d36d812595c5f45c31c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8da\/8da03aa5f2ca4d36d812595c5f45c31c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u043c\u0443 \u043f\u043e\u043b\u044e. \u041f\u0440\u0438\u0447\u0438\u043d\u0430 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u(x)=2\\sqrt{|x|}\" alt=\"u(x)=2\\sqrt{|x|}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab9\/ab98f55e1accaf9e283dc920358e7587.svg\" width=\"107\" height=\"34\" data-width=\"13.356\" data-height=\"4.208\" data-vertical-align=\"-1.538\" style=\"width: 13.356ex; height: 4.208ex; vertical-align: -1.538ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab9\/ab98f55e1accaf9e283dc920358e7587.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ab\/ab9\/ab98f55e1accaf9e283dc920358e7587.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e \u043b\u0438\u043f\u0448\u0438\u0446\u0435\u0432\u043e\u0439 \u0432 \u043e\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0441\u0442\u0438 \u0442\u043e\u0447\u043a\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x=0\" alt=\"x=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e11\/e11729b0b65ecade3fc272548a3883fc.svg\" width=\"44\" height=\"14\" data-width=\"5.442\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 5.442ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e11\/e11729b0b65ecade3fc272548a3883fc.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e11\/e11729b0b65ecade3fc272548a3883fc.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u041d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u043d\u0430\u0448 \u0441\u0435\u0442\u0430\u043f \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442 \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0441\u0442\u0438 (\u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0438\u0437 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u041a\u043e\u0448\u0438 \u2014 \u041b\u0438\u043f\u0448\u0438\u0446\u0430), \u043f\u0440\u0438\u043c\u0435\u043c \u044d\u0442\u043e \u0437\u0430 \u0444\u0430\u043a\u0442 \u043d\u0435 \u0431\u0443\u0434\u0435\u043c \u043a \u043d\u0435\u043c\u0443 \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0442\u044c\u0441\u044f \u0434\u0430\u043b\u0435\u0435 \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 \ud83d\ude42<\/p>\n<\/div>\n<\/details>\n<p>\u0418\u043c\u0435\u043d\u043d\u043e \u044d\u0442\u043e \u0438 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442, \u043f\u043e\u0447\u0435\u043c\u0443 \u043c\u043e\u0436\u043d\u043e \u0434\u0432\u0438\u0433\u0430\u0442\u044c\u0441\u044f \u043f\u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c\u0443 \u043f\u043e\u043b\u044e. \u041c\u044b \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u00ab\u043d\u0430 \u0433\u043b\u0430\u0437\u00bb \u0437\u0430\u043c\u0435\u043d\u0438\u043b\u0438 \u0440\u0430\u0437\u043d\u044b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043d\u0430 \u0441\u0440\u0435\u0434\u043d\u044e\u044e. \u041c\u044b \u043f\u043e\u043a\u0430\u0437\u0430\u043b\u0438, \u0447\u0442\u043e \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0441 \u043f\u0440\u044f\u043c\u044b\u043c\u0438 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f\u043c\u0438 \u0438 \u043d\u043e\u0432\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0434\u0432\u0438\u0436\u0435\u0442\u0441\u044f \u043f\u043e ODE, \u043f\u043e\u0440\u043e\u0436\u0434\u0430\u044e\u0442 \u043e\u0434\u043d\u0443 \u0438 \u0442\u0443 \u0436\u0435 \u044d\u0432\u043e\u043b\u044e\u0446\u0438\u044e \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{d \\tilde{x}_t}{dt} = u^*(\\tilde{x}_t,t),\" alt=\"\\frac{d \\tilde{x}_t}{dt} = u^*(\\tilde{x}_t,t),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c42\/c420e641bf7eaf86433a2c4aa67bcb1b.svg\" width=\"126\" height=\"38\" data-width=\"15.802\" data-height=\"4.803\" data-vertical-align=\"-1.836\" style=\"width: 15.802ex; height: 4.803ex; vertical-align: -1.836ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c42\/c420e641bf7eaf86433a2c4aa67bcb1b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c42\/c420e641bf7eaf86433a2c4aa67bcb1b.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0432 \u043e\u0434\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0440\u0430\u0437\u043d\u044b\u0435 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u043c\u043e\u0433\u0443\u0442 \u0438\u043c\u0435\u0442\u044c \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438. \u041e\u0434\u043d\u0438 \u043b\u0435\u0442\u044f\u0442 \u043b\u0435\u0432\u0435\u0435, \u0434\u0440\u0443\u0433\u0438\u0435 \u2014 \u043f\u0440\u0430\u0432\u0435\u0435. \u041e\u0434\u043d\u0438 \u0431\u044b\u0441\u0442\u0440\u0435\u0435, \u0434\u0440\u0443\u0433\u0438\u0435 \u2014 \u043c\u0435\u0434\u043b\u0435\u043d\u043d\u0435\u0435. \u041d\u043e \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043d\u0435 \u043e\u0442 \u0438\u043d\u0434\u0438\u0432\u0438\u0434\u0443\u0430\u043b\u044c\u043d\u043e\u0439 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043a\u0430\u0436\u0434\u043e\u0439 \u0447\u0430\u0441\u0442\u0438\u0446\u044b, \u0430 \u043e\u0442 \u0441\u0443\u043c\u043c\u0430\u0440\u043d\u043e\u0433\u043e \u043f\u043e\u0442\u043e\u043a\u0430 \u043c\u0430\u0441\u0441\u044b \u0447\u0435\u0440\u0435\u0437 \u044d\u0442\u0443 \u0442\u043e\u0447\u043a\u0443. \u041e\u043d \u0440\u0430\u0432\u0435\u043d:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"p_t(x)u^*(x,t).\" alt=\"p_t(x)u^*(x,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acf\/acf026af99f647dfefe2d8b435e2937c.svg\" width=\"102\" height=\"18\" data-width=\"12.745\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 12.745ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acf\/acf026af99f647dfefe2d8b435e2937c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acf\/acf026af99f647dfefe2d8b435e2937c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u044d\u0442\u043e\u043c\u0443 Flow Matching \u0443\u0447\u0438\u0442 \u043c\u0430\u043a\u0440\u043e\u0441\u043a\u043e\u043f\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u043e\u043b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"u^*(x,t)\" alt=\"u^*(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg\" width=\"57\" height=\"18\" data-width=\"7.159\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.159ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u043d\u0435 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043c\u0435\u0436\u0434\u0443 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0430\u0440\u0430\u043c\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"(x_0,x_1)\" alt=\"(x_0,x_1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg\" width=\"59\" height=\"18\" data-width=\"7.33\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.33ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b8\/8b85d361e914f7910933caca8fc57c75.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0414\u0432\u0438\u0433\u0430\u044f\u0441\u044c \u043f\u043e \u044d\u0442\u043e\u043c\u0443 \u0441\u0440\u0435\u0434\u043d\u0435\u043c\u0443 \u043f\u043e\u043b\u044e \u0438\u0437 \u0448\u0443\u043c\u0430, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0442\u0443 \u0436\u0435 \u044d\u0432\u043e\u043b\u044e\u0446\u0438\u044e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439, \u0447\u0442\u043e \u0438 \u043f\u0440\u0438 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0438 \u0432\u0441\u0435\u0445 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u0445 \u043f\u0430\u0440 \u043f\u043e \u043f\u0440\u044f\u043c\u044b\u043c \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f\u043c.<\/p>\n<\/div>\n<\/details>\n<p>\u0418\u0442\u0430\u043a, \u043f\u0435\u0440\u0432\u0430\u044f \u0447\u0430\u0441\u0442\u044c \u043f\u0440\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 Flow Matching \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0430. \u041c\u044b \u043f\u043e\u043a\u0430\u0437\u0430\u043b\u0438, \u0447\u0442\u043e \u0441\u0443\u0442\u044c Flow Matching\u2019\u0430 \u2014 \u0432\u044b\u0443\u0447\u0438\u0432\u0430\u043d\u0438\u0435 \u0441\u0440\u0435\u0434\u043d\u0438\u0445 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439. \u0421\u0430\u043c\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u043e\u0431\u043d\u043e\u0432\u0438\u0442\u044c \u0447\u0430\u0439 \u0438 \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043a\u043e \u0432\u0442\u043e\u0440\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u2014 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 \u0432 \u043e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440! \ud83d\ude07<\/p>\n<h2>\u041c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u044f<\/h2>\n<p>\u0418\u0442\u0430\u043a, \u043c\u044b \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 Flow Matching. \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043f\u043e\u0447\u0435\u043c\u0443 \u0435\u0433\u043e \u043d\u0435 \u043e\u0447\u0435\u043d\u044c \u0443\u0434\u043e\u0431\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \ud83d\ude22<\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f Flow Matching-\u043c\u043e\u0434\u0435\u043b\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044f \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u0445 \u0448\u0430\u0433\u043e\u0432. \u041c\u044b \u0441\u0442\u0430\u0440\u0442\u0443\u0435\u043c \u0438\u0437 \u0448\u0443\u043c\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_0 \\sim \\mathcal{N}(0,I)\" alt=\"x_0 \\sim \\mathcal{N}(0,I)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg\" width=\"100\" height=\"19\" data-width=\"12.552\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.552ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cb\/cb4\/cb4b0a180c73061f7ea3251505554470.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e \u0434\u0432\u0438\u0436\u0435\u043c\u0441\u044f \u043f\u043e \u0432\u044b\u0443\u0447\u0435\u043d\u043d\u043e\u043c\u0443 \u043f\u043e\u043b\u044e <img decoding=\"async\" class=\"formula inline\" source=\"u_{\\theta}(x,t)\" alt=\"u_{\\theta}(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg\" width=\"57\" height=\"18\" data-width=\"7.109\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.109ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f0\/f06\/f06f1803f85c98cfd0abe5a6a5c746e7.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"t=0\" alt=\"t=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e <img decoding=\"async\" class=\"formula inline\" source=\"t=1\" alt=\"t=1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_{t+\\Delta t} = x_t + \\Delta t \\cdot u_\\theta(x_t,t).\" alt=\"x_{t+\\Delta t} = x_t + \\Delta t \\cdot u_\\theta(x_t,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/69\/690\/690d5c8c741b4e879f798f3f614c79ad.svg\" width=\"207\" height=\"18\" data-width=\"25.896\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 25.896ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/69\/690\/690d5c8c741b4e879f798f3f614c79ad.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/69\/690\/690d5c8c741b4e879f798f3f614c79ad.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043e\u0431\u044b\u0447\u043d\u043e \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u043c\u043d\u043e\u0433\u043e \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0445 \u0448\u0430\u0433\u043e\u0432. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0435\u0441\u043b\u0438 \u0432\u0437\u044f\u0442\u044c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\Delta t = 0.01,\" alt=\"\\Delta t = 0.01,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/88\/88a\/88ad18384e3f9b1ed5d9a640f15d8c63.svg\" width=\"83\" height=\"18\" data-width=\"10.37\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 10.37ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/88\/88a\/88ad18384e3f9b1ed5d9a640f15d8c63.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/88\/88a\/88ad18384e3f9b1ed5d9a640f15d8c63.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e \u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"[0,1]\" alt=\"[0,1]\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/ccf\/ccfcd347d0bf65dc77afe01a3306a96b.svg\" width=\"36\" height=\"18\" data-width=\"4.526\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 4.526ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/ccf\/ccfcd347d0bf65dc77afe01a3306a96b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/ccf\/ccfcd347d0bf65dc77afe01a3306a96b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u0441\u044f <img decoding=\"async\" class=\"formula inline\" source=\"100\" alt=\"100\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f8\/f89\/f899139df5e1059396431415e770c6dd.svg\" width=\"27\" height=\"12\" data-width=\"3.394\" data-height=\"1.557\" data-vertical-align=\"-0.05\" style=\"width: 3.394ex; height: 1.557ex; vertical-align: -0.05ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f8\/f89\/f899139df5e1059396431415e770c6dd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f8\/f89\/f899139df5e1059396431415e770c6dd.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0448\u0430\u0433\u043e\u0432. \u0422\u043e \u0435\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"100\" alt=\"100\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f8\/f89\/f899139df5e1059396431415e770c6dd.svg\" width=\"27\" height=\"12\" data-width=\"3.394\" data-height=\"1.557\" data-vertical-align=\"-0.05\" style=\"width: 3.394ex; height: 1.557ex; vertical-align: -0.05ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f8\/f89\/f899139df5e1059396431415e770c6dd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f8\/f89\/f899139df5e1059396431415e770c6dd.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u0431\u0440\u0430\u0449\u0435\u043d\u0438\u0439 \u043a \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u0438 \u0434\u043b\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u043e\u0434\u043d\u043e\u0433\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f. \u0410 \u044d\u0442\u043e \u043e\u0447\u0435\u043d\u044c \u043c\u043d\u043e\u0433\u043e.<\/p>\n<p>\u0417\u0434\u0435\u0441\u044c \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u044e\u0442 \u0434\u0432\u0435 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b:<\/p>\n<ol>\n<li>\n<p><strong>\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c.<\/strong> \u041a\u0430\u0436\u0434\u044b\u0439 \u0448\u0430\u0433 \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0437\u0430\u043f\u0443\u0441\u043a\u0430 \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u0438. \u0414\u0430\u0436\u0435 \u0435\u0441\u043b\u0438 \u043e\u0434\u0438\u043d \u043f\u0440\u043e\u0445\u043e\u0434 \u043c\u043e\u0434\u0435\u043b\u0438 \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0431\u044b\u0441\u0442\u0440\u043e \u2014 \u0434\u0435\u0441\u044f\u0442\u043a\u0438 \u0438\u043b\u0438 \u0441\u043e\u0442\u043d\u0438 \u043f\u0440\u043e\u0445\u043e\u0434\u043e\u0432 \u043c\u043e\u0433\u0443\u0442 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044e \u0441\u043b\u0438\u0448\u043a\u043e\u043c \u043c\u0435\u0434\u043b\u0435\u043d\u043d\u043e\u0439 \u0434\u043b\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f.<\/p>\n<\/li>\n<li>\n<p><strong>\u041e\u0448\u0438\u0431\u043a\u0430 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u0438\u0437\u0430\u0446\u0438\u0438.<\/strong> \u0412 \u0438\u0434\u0435\u0430\u043b\u0435 \u043c\u044b \u0445\u043e\u0442\u0435\u043b\u0438 \u0431\u044b \u0434\u0432\u0438\u0433\u0430\u0442\u044c\u0441\u044f \u043f\u043e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438. \u041d\u043e \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u043c\u044b \u0434\u0435\u043b\u0430\u0435\u043c \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u0448\u0430\u0433\u0438 \u0440\u0430\u0437\u043c\u0435\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"\\Delta t\" alt=\"\\Delta t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5a\/5a7\/5a72f1304af0783657605aed0e38201a.svg\" width=\"22\" height=\"18\" data-width=\"2.701\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.701ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5a\/5a7\/5a72f1304af0783657605aed0e38201a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5a\/5a7\/5a72f1304af0783657605aed0e38201a.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0415\u0441\u043b\u0438 \u0448\u0430\u0433 \u0441\u043b\u0438\u0448\u043a\u043e\u043c \u0431\u043e\u043b\u044c\u0448\u043e\u0439, \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u0437\u0430\u043c\u0435\u0442\u043d\u043e \u043e\u0442\u043a\u043b\u043e\u043d\u044f\u0442\u044c\u0441\u044f \u043e\u0442 \u0442\u043e\u0439, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0437\u0430\u0434\u0430\u0451\u0442 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0435 \u043f\u043e\u043b\u0435. \u042d\u0442\u043e \u043c\u043e\u0436\u0435\u0442 \u0443\u0445\u0443\u0434\u0448\u0430\u0442\u044c \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f.<\/p>\n<\/li>\n<\/ol>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/8e2\/4b2\/4c0\/8e24b24c01ea26770e22382b544ac290.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 19. \u041e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043e\u0442 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u043f\u0440\u0438 \u043a\u0440\u0443\u043f\u043d\u044b\u0445 \u0448\u0430\u0433\u0430\u0445 \u0438 \u043f\u0440\u0438\u0445\u043e\u0434 \u0432 \u0434\u0440\u0443\u0433\u0443\u044e \u043a\u043e\u043d\u0435\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \\hat{x}_1. \u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0441\u0447\u0438\u0442\u0430\u0435\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u044b\u043c: \u043f\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u043e\u0441\u0438 \u2014 \u0432\u0440\u0435\u043c\u044f, \u043f\u043e \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0439 \u2014 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/8e2\/4b2\/4c0\/8e24b24c01ea26770e22382b544ac290.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/8e2\/4b2\/4c0\/8e24b24c01ea26770e22382b544ac290.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 19. \u041e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043e\u0442 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u043f\u0440\u0438 \u043a\u0440\u0443\u043f\u043d\u044b\u0445 \u0448\u0430\u0433\u0430\u0445 \u0438 \u043f\u0440\u0438\u0445\u043e\u0434 \u0432 \u0434\u0440\u0443\u0433\u0443\u044e \u043a\u043e\u043d\u0435\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \\hat{x}_1. \u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0441\u0447\u0438\u0442\u0430\u0435\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u044b\u043c: \u043f\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u043e\u0441\u0438 \u2014 \u0432\u0440\u0435\u043c\u044f, \u043f\u043e \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0439 \u2014 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430<\/figcaption><\/div>\n<\/figure>\n<h3>\u0414\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f<\/h3>\n<p>\u041e\u0442\u0441\u044e\u0434\u0430 \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442 \u0438\u0434\u0435\u044f \u2014 \u043d\u0430\u0443\u0447\u0438\u0442\u044c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0431\u0443\u0434\u0435\u0442 \u0441\u0440\u0430\u0437\u0443 \u0432\u044b\u0443\u0447\u0438\u0432\u0430\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044e \u043a\u0430\u0440\u0442\u0438\u043d\u043e\u043a. \u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u0431\u0443\u0447\u0438\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u0440\u0430\u0437\u0443 \u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0444\u0438\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z), \\qquad z \\sim \\mathcal{N}(0,I_m).\" alt=\"\\hat{x}_1 = G_\\phi(z), \\qquad z \\sim \\mathcal{N}(0,I_m).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c94\/c947739b045c8e2b7423f4b55ec75563.svg\" width=\"240\" height=\"20\" data-width=\"29.96\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 29.96ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c94\/c947739b045c8e2b7423f4b55ec75563.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c94\/c947739b045c8e2b7423f4b55ec75563.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a\u043e\u0439 \u043f\u043e\u0434\u0445\u043e\u0434 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0435\u0439<\/strong>: \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u043d\u0443\u044e \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u0443\u044e Flow Matching-\u043c\u043e\u0434\u0435\u043b\u044c \u043a\u0430\u043a \u0443\u0447\u0438\u0442\u0435\u043b\u044f \u0438 \u043f\u044b\u0442\u0430\u0435\u043c\u0441\u044f \u043f\u0435\u0440\u0435\u0434\u0430\u0442\u044c \u0435\u0451 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0431\u043e\u043b\u0435\u0435 \u0431\u044b\u0441\u0442\u0440\u043e\u0439 \u043e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438-\u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0443.<\/p>\n<p>\u041e\u0431\u044b\u0447\u043d\u043e \u043f\u043e\u0434 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0435\u0439 \u043f\u043e\u043d\u0438\u043c\u0430\u044e\u0442 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438 \u043f\u043e \u0432\u044b\u0445\u043e\u0434\u0430\u043c \u0431\u043e\u043b\u044c\u0448\u043e\u0439, \u043d\u043e \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u0432 \u0432\u0438\u0434\u0443 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u043e\u0433\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 (\u0441\u0430\u043c\u0430 \u043c\u043e\u0434\u0435\u043b\u044c-\u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0431\u043e\u043b\u044c\u0448\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 \u0443\u0447\u0438\u0442\u0435\u043b\u044f).<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/131\/8e9\/a69\/1318e9a691ebc5ab45a8701f0ea43ac9.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 20. \u0414\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f \u0443\u0447\u0438\u0442 \u043e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 G_\\phi \u0434\u0435\u043b\u0430\u0442\u044c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 p_G \u0431\u043b\u0438\u0436\u0435 \u043a \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u0434\u0430\u043d\u043d\u044b\u0445 p_1, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u043c \u0443\u0447\u0438\u0442\u0435\u043b\u0435\u043c\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/131\/8e9\/a69\/1318e9a691ebc5ab45a8701f0ea43ac9.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/131\/8e9\/a69\/1318e9a691ebc5ab45a8701f0ea43ac9.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 20. \u0414\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f \u0443\u0447\u0438\u0442 \u043e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 G_\\phi \u0434\u0435\u043b\u0430\u0442\u044c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 p_G \u0431\u043b\u0438\u0436\u0435 \u043a \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u0434\u0430\u043d\u043d\u044b\u0445 p_1, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u043c \u0443\u0447\u0438\u0442\u0435\u043b\u0435\u043c<\/figcaption><\/div>\n<\/figure>\n<p>\u0412\u0430\u0436\u043d\u043e\u0435 \u0443\u0442\u043e\u0447\u043d\u0435\u043d\u0438\u0435 \u2014 \u043c\u044b \u043d\u0435 \u0445\u043e\u0442\u0438\u043c \u0432\u044b\u0443\u0447\u0438\u0442\u044c \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0438\u0437 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0431\u044b \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u043b\u043e \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u0435 Flow Matching\u2019\u0430. \u0423 \u043d\u0430\u0441 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0441\u043e \u0441\u0432\u043e\u0438\u043c \u043b\u0430\u0442\u0435\u043d\u0442\u043d\u044b\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e\u043c <img decoding=\"async\" class=\"formula inline\" source=\"z\" alt=\"z\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg\" width=\"12\" height=\"12\" data-width=\"1.052\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.052ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043d\u0435 \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u044b\u043c \u0441 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> (\u043c\u043e\u0436\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0434\u0430\u0436\u0435 \u0434\u0440\u0443\u0433\u0443\u044e \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c). \u041d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u043c\u044b \u0441\u0434\u0435\u043b\u0430\u0435\u043c \u0447\u0442\u043e-\u0442\u043e \u043f\u043e\u0445\u043e\u0436\u0435\u0435 \u043d\u0430 <a href=\"https:\/\/arxiv.org\/pdf\/1406.2661\" rel=\"noopener nofollow\">GAN<\/a>, \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u0442\u043e\u0440 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0438\u043c\u0435\u0435\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0439 \u0432\u0438\u0434 \u0438 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0441\u0442\u043e\u0445\u0430\u0441\u0442\u0438\u0447\u043d\u043e\u0441\u0442\u044c \u0438\u0437-\u0437\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0415\u0441\u0442\u044c \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <a href=\"https:\/\/arxiv.org\/pdf\/2303.01469\" rel=\"noopener nofollow\">consistency models<\/a>, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u0442\u0430\u0432\u044f\u0442 \u0441\u0432\u043e\u0435\u0439 \u0437\u0430\u0434\u0430\u0447\u0435\u0439 \u0432\u044b\u0443\u0447\u0438\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G: x_0 \u2192 x_1\" alt=\"G: x_0 \u2192 x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0b\/0bc\/0bc0c90f63817e67c6cba0fb50ddcbca.svg\" width=\"94\" height=\"16\" data-width=\"11.747\" data-height=\"1.97\" data-vertical-align=\"-0.375\" style=\"width: 11.747ex; height: 1.97ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0b\/0bc\/0bc0c90f63817e67c6cba0fb50ddcbca.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0b\/0bc\/0bc0c90f63817e67c6cba0fb50ddcbca.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1\" alt=\"\\hat{x}_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg\" width=\"18\" height=\"19\" data-width=\"2.282\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.282ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0439 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0434\u0432\u0438\u0433\u0430\u044f\u0441\u044c \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"u_\\theta(x_t, t)\" alt=\"u_\\theta(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg\" width=\"63\" height=\"18\" data-width=\"7.875\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.875ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/092\/09245c24a7715698584e3c4e83901a46.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043b\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u^*(x_t, t)\" alt=\"u^*(x_t, t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fab\/fabd937d05e58aa0cac624c864a0be69.svg\" width=\"63\" height=\"18\" data-width=\"7.924\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.924ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fab\/fabd937d05e58aa0cac624c864a0be69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fa\/fab\/fabd937d05e58aa0cac624c864a0be69.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043d\u043e \u044d\u0442\u043e \u0443\u0436\u0435 \u0442\u0435\u043c\u0430 \u0434\u043b\u044f \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u0441\u0442\u0430 \ud83d\ude42.<\/p>\n<h4>\u041f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435 \u043f\u043e\u043b\u044f \u043f\u043e \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u043c \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0430\u043c<\/h4>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u043e\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435 \u043f\u043e Flow Matching-\u043f\u043e\u043b\u044e \u043e\u0434\u043d\u0438\u043c \u043f\u0440\u044f\u043c\u044b\u043c \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u043e\u043c \u043e\u0442 \u0448\u0443\u043c\u0430 \u043a \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044e.<\/p>\n<p>\u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"G_\\phi : \\mathbb{R}^m \\to \\mathbb{R}^d,\" alt=\"G_\\phi : \\mathbb{R}^m \\to \\mathbb{R}^d,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b4\/8b42e20dca58e4a499a32c425991fbb8.svg\" width=\"119\" height=\"22\" data-width=\"14.833\" data-height=\"2.712\" data-vertical-align=\"-0.79\" style=\"width: 14.833ex; height: 2.712ex; vertical-align: -0.79ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b4\/8b42e20dca58e4a499a32c425991fbb8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8b\/8b4\/8b42e20dca58e4a499a32c425991fbb8.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041e\u043d \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442 \u043d\u0430 \u0432\u0445\u043e\u0434 \u043b\u0430\u0442\u0435\u043d\u0442\u043d\u044b\u0439 \u0448\u0443\u043c (\u0435\u0433\u043e \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u043c\u043e\u0436\u0435\u0442 \u043e\u0442\u043b\u0438\u0447\u0430\u0442\u044c\u0441\u044f \u043e\u0442 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\" alt=\"x_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.339\" data-vertical-align=\"-0.339\" style=\"width: 2.282ex; height: 1.339ex; vertical-align: -0.339ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/aa\/aa6\/aa687da0086c1ea060a8838e24611319.svg 781w\" loading=\"lazy\" decode=\"async\"\/>):<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"z \\sim \\mathcal{N}(0,I_m)\" alt=\"z \\sim \\mathcal{N}(0,I_m)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg\" width=\"102\" height=\"19\" data-width=\"12.769\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.769ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418 \u0441\u0440\u0430\u0437\u0443 \u0432\u044b\u0434\u0430\u0451\u0442 \u043e\u0431\u044a\u0435\u043a\u0442 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0434\u0430\u043d\u043d\u044b\u0445:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z) \\in \\mathbb{R}^d.\" alt=\"\\hat{x}_1 = G_\\phi(z) \\in \\mathbb{R}^d.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a60\/a60bdcf4a2c019242174179512278936.svg\" width=\"137\" height=\"22\" data-width=\"17.079\" data-height=\"2.712\" data-vertical-align=\"-0.79\" style=\"width: 17.079ex; height: 2.712ex; vertical-align: -0.79ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a60\/a60bdcf4a2c019242174179512278936.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a60\/a60bdcf4a2c019242174179512278936.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u0434\u0435\u0441\u044c <img decoding=\"async\" class=\"formula inline\" source=\"m\" alt=\"m\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg\" width=\"16\" height=\"12\" data-width=\"1.986\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.986ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u043b\u0430\u0442\u0435\u043d\u0442\u043d\u043e\u0433\u043e \u0448\u0443\u043c\u0430 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430, \u0430 <img decoding=\"async\" class=\"formula inline\" source=\"d\" alt=\"d\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/82\/827\/8277e0910d750195b448797616e091ad.svg\" width=\"12\" height=\"13\" data-width=\"1.176\" data-height=\"1.593\" data-vertical-align=\"-0.023\" style=\"width: 1.176ex; height: 1.593ex; vertical-align: -0.023ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/82\/827\/8277e0910d750195b448797616e091ad.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/82\/827\/8277e0910d750195b448797616e091ad.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u0434\u0430\u043d\u043d\u044b\u0445. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0435\u0441\u043b\u0438 \u043c\u044b \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u043c \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c <img decoding=\"async\" class=\"formula inline\" source=\"32\\times32\\times3\" alt=\"32\\times32\\times3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78a\/78a8782a4d5aecf7ac8ab1a57ef1c5d4.svg\" width=\"90\" height=\"18\" data-width=\"11.188\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 11.188ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78a\/78a8782a4d5aecf7ac8ab1a57ef1c5d4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78a\/78a8782a4d5aecf7ac8ab1a57ef1c5d4.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"d=3072\" alt=\"d=3072\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/078\/07854078e5be09c0e63d23179db43045.svg\" width=\"70\" height=\"14\" data-width=\"8.718\" data-height=\"1.756\" data-vertical-align=\"-0.186\" style=\"width: 8.718ex; height: 1.756ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/078\/07854078e5be09c0e63d23179db43045.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/078\/07854078e5be09c0e63d23179db43045.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"m\" alt=\"m\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg\" width=\"16\" height=\"12\" data-width=\"1.986\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.986ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8f57715090da2632453988d9a1501b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0431\u0440\u0430\u0442\u044c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e.<\/p>\n<p>\u0412\u043e \u0432\u0440\u0435\u043c\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u043d\u0430\u043c \u043d\u0443\u0436\u0435\u043d \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0434\u0438\u043d \u0437\u0430\u043f\u0443\u0441\u043a \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430: \u043c\u044b \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"z\" alt=\"z\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg\" width=\"12\" height=\"12\" data-width=\"1.052\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.052ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0441\u0447\u0438\u0442\u0430\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi(z)\" alt=\"G_\\phi(z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg\" width=\"46\" height=\"19\" data-width=\"5.732\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 5.732ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0441\u0440\u0430\u0437\u0443 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435. \u041d\u043e \u0434\u043b\u044f \u0435\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0443\u0436\u043d\u043e \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435, \u043a\u0430\u043a \u0438 \u0434\u043b\u044f Flow Matching\u2019\u0430.<\/p>\n<p>\u0418\u0434\u0435\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u2014 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043f\u043e\u043b\u044f, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0443, \u0434\u043e\u043b\u0436\u043d\u044b \u0431\u044b\u0442\u044c \u043f\u043e\u0445\u043e\u0436\u0438 \u043d\u0430 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u0435 Flow Matching-\u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 (\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u043f\u043e \u043f\u043e\u043b\u044e, \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u043d\u043e\u043c\u0443 \u0438\u0437 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445). \u0422\u043e\u0433\u0434\u0430 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0438 \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0435 \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0438 \u0441\u043e\u0432\u043f\u0430\u0434\u0443\u0442.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/5b6\/5d1\/a4a\/5b65d1a4af15ab2d56ab16f2567de46d.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 21. \u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0434\u0432\u0443\u0445 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u0448\u0443\u043c\u043e\u0432: z \u0437\u0430\u0434\u0430\u0451\u0442 \u0444\u0438\u043d\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \\hat{x}1=G\\phi(z), \u0430 x_0 \u2014 \u043d\u0430\u0447\u0430\u043b\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0434\u0430\u043d\u043d\u044b\u0445\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/5b6\/5d1\/a4a\/5b65d1a4af15ab2d56ab16f2567de46d.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/5b6\/5d1\/a4a\/5b65d1a4af15ab2d56ab16f2567de46d.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 21. \u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0434\u0432\u0443\u0445 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u0448\u0443\u043c\u043e\u0432: z \u0437\u0430\u0434\u0430\u0451\u0442 \u0444\u0438\u043d\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \\hat{x}1=G\\phi(z), \u0430 x_0 \u2014 \u043d\u0430\u0447\u0430\u043b\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0434\u0430\u043d\u043d\u044b\u0445<\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u0430\u0447\u043d\u0451\u043c \u0441 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f \u043f\u043e\u043b\u044f \u0434\u043b\u044f \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043a\u0430\u0440\u0442\u0438\u043d\u043e\u043a. \u041f\u043e\u0432\u0442\u043e\u0440\u0438\u043c (\u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438) \u0432\u044b\u0432\u043e\u0434, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u044b \u0434\u0435\u043b\u0430\u043b\u0438 \u0434\u043b\u044f Flow Matching\u2019\u0430, \u043d\u043e \u0434\u043b\u044f \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0439, \u043d\u0435 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u0434\u0432\u0430 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u0448\u0443\u043c\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m).\" alt=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6a8\/6a81e792329bbe24b54011a6ee976562.svg\" width=\"259\" height=\"19\" data-width=\"32.356\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 32.356ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6a8\/6a81e792329bbe24b54011a6ee976562.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6a8\/6a81e792329bbe24b54011a6ee976562.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0428\u0443\u043c <img decoding=\"async\" class=\"formula inline\" source=\"z\" alt=\"z\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg\" width=\"12\" height=\"12\" data-width=\"1.052\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.052ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e\u0434\u0430\u0451\u0442\u0441\u044f \u0432 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0438 \u0437\u0430\u0434\u0430\u0451\u0442 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z) \\in \\mathbb{R}^d.\" alt=\"\\hat{x}_1 = G_\\phi(z) \\in \\mathbb{R}^d.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a60\/a60bdcf4a2c019242174179512278936.svg\" width=\"137\" height=\"22\" data-width=\"17.079\" data-height=\"2.712\" data-vertical-align=\"-0.79\" style=\"width: 17.079ex; height: 2.712ex; vertical-align: -0.79ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a60\/a60bdcf4a2c019242174179512278936.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a60\/a60bdcf4a2c019242174179512278936.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0410 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0439 \u0448\u0443\u043c <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u043a\u0430\u043a \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0434\u0430\u043d\u043d\u044b\u0445. \u041c\u0435\u0436\u0434\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1\" alt=\"\\hat{x}_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg\" width=\"18\" height=\"19\" data-width=\"2.282\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.282ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u044f\u043c\u0443\u044e:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_t = (1-t)x_0 + t\\hat{x}_1, \\qquad t\\in[0,1].\" alt=\"\\hat{x}_t = (1-t)x_0 + t\\hat{x}_1, \\qquad t\\in[0,1].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f16\/f162cdf7fb46ea3325995e99ec6adb56.svg\" width=\"272\" height=\"19\" data-width=\"33.965\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 33.965ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f16\/f162cdf7fb46ea3325995e99ec6adb56.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f16\/f162cdf7fb46ea3325995e99ec6adb56.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a \u043a\u0430\u043a \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1\" alt=\"\\hat{x}_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg\" width=\"18\" height=\"19\" data-width=\"2.282\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.282ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043b\u0435\u0436\u0430\u0442 \u0432 <img decoding=\"async\" class=\"formula inline\" source=\"\\mathbb{R}^d\" alt=\"\\mathbb{R}^d\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/19\/19a\/19ad202815dcdc697be0ca2f8af02ed7.svg\" width=\"21\" height=\"21\" data-width=\"2.653\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 2.653ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/19\/19a\/19ad202815dcdc697be0ca2f8af02ed7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/19\/19a\/19ad202815dcdc697be0ca2f8af02ed7.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0432\u0441\u044f \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u043e\u0436\u0435 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0434\u0430\u043d\u043d\u044b\u0445:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_t \\in \\mathbb{R}^d.\" alt=\"\\hat{x}_t \\in \\mathbb{R}^d.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/ce\/ce7\/ce755b168f8ba0e332f239fc4c7b3be9.svg\" width=\"65\" height=\"21\" data-width=\"8.108\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 8.108ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/ce\/ce7\/ce755b168f8ba0e332f239fc4c7b3be9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/ce\/ce7\/ce755b168f8ba0e332f239fc4c7b3be9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0421\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0432\u0434\u043e\u043b\u044c \u044d\u0442\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial \\hat{x}_t}{\\partial t} = \\hat{x}_1 - x_0 = G_\\phi(z)-x_0.\" alt=\"\\frac{\\partial \\hat{x}_t}{\\partial t} = \\hat{x}_1 - x_0 = G_\\phi(z)-x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/be\/be0\/be0d742fd7091fbd25cb8b24555226b4.svg\" width=\"233\" height=\"40\" data-width=\"29.107\" data-height=\"4.964\" data-vertical-align=\"-1.916\" style=\"width: 29.107ex; height: 4.964ex; vertical-align: -1.916ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/be\/be0\/be0d742fd7091fbd25cb8b24555226b4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/be\/be0\/be0d742fd7091fbd25cb8b24555226b4.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\ud83d\udca1 \u0412\u0430\u0436\u043d\u043e: <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"z\" alt=\"z\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg\" width=\"12\" height=\"12\" data-width=\"1.052\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.052ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0440\u0430\u0437\u043d\u044b\u0435 \u0448\u0443\u043c\u044b.<\/p>\n<p>\u0428\u0443\u043c <img decoding=\"async\" class=\"formula inline\" source=\"z\" alt=\"z\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg\" width=\"12\" height=\"12\" data-width=\"1.052\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.052ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0436\u0438\u0432\u0451\u0442 \u0432 \u043b\u0430\u0442\u0435\u043d\u0442\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"\\mathbb{R}^m\" alt=\"\\mathbb{R}^m\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2a\/2ab\/2ab1d8efc486f74009b31e6f64106011.svg\" width=\"26\" height=\"18\" data-width=\"3.226\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 3.226ex; height: 2.262ex; 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srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6fd\/6fd85a3d9abb649d51e5d5cc3e05b231.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6fd\/6fd85a3d9abb649d51e5d5cc3e05b231.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0428\u0443\u043c <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0436\u0438\u0432\u0451\u0442 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\u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0433\u043e \u0448\u0443\u043c\u0430 \u043a \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430.<\/p>\n<p>\u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t=0\" alt=\"t=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e8\/3e8f7b0adf6d7024b951f29a18225e4a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u043e\u0431\u044b\u0447\u043d\u044b\u0439 \u0448\u0443\u043c \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0434\u0430\u043d\u043d\u044b\u0445:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_0 = x_0 \\sim \\mathcal{N}(0,I_d),\" alt=\"\\hat{x}_0 = x_0 \\sim \\mathcal{N}(0,I_d),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/61\/61d\/61d4ceea3ba3e3e5cf0c5ddd90bc242c.svg\" width=\"155\" height=\"19\" data-width=\"19.354\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 19.354ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/61\/61d\/61d4ceea3ba3e3e5cf0c5ddd90bc242c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/61\/61d\/61d4ceea3ba3e3e5cf0c5ddd90bc242c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0410 \u043f\u0440\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t=1\" alt=\"t=1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg\" width=\"40\" height=\"14\" data-width=\"4.965\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.965ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b73\/b73c3280b6f85a6ac520af103083f535.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043e\u0431\u044a\u0435\u043a\u0442 \u0438\u0437 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z).\" alt=\"\\hat{x}_1 = G_\\phi(z).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg\" width=\"93\" height=\"20\" data-width=\"11.66\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 11.66ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0443 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0442\u043e\u0436\u0435 \u0435\u0441\u0442\u044c \u0441\u0432\u043e\u0451 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439. \u0412 \u043e\u0434\u043d\u043e\u0439 \u0438 \u0442\u043e\u0439 \u0436\u0435 \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u043e\u0433\u0443\u0442 \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442\u044c \u0440\u0430\u0437\u043d\u044b\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u2014 \u043e\u043d\u0438 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u044b \u0438\u0437 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u043f\u0430\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"(x_0,z)\" alt=\"(x_0,z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afa\/afa910e6a7af91b3309438ff9c670a68.svg\" width=\"49\" height=\"18\" data-width=\"6.1\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.1ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afa\/afa910e6a7af91b3309438ff9c670a68.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afa\/afa910e6a7af91b3309438ff9c670a68.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043a\u0430\u043a \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^\\phi(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ G_\\phi(z)-x_0 \\mid \\hat{x}_t = x \\right].\" alt=\"u^\\phi(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ G_\\phi(z)-x_0 \\mid \\hat{x}_t = x \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/16\/162\/16247548de83b25ed65addee24256de7.svg\" width=\"408\" height=\"23\" data-width=\"50.99\" data-height=\"2.907\" data-vertical-align=\"-0.888\" style=\"width: 50.99ex; height: 2.907ex; vertical-align: -0.888ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/16\/162\/16247548de83b25ed65addee24256de7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/16\/162\/16247548de83b25ed65addee24256de7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041e\u043d\u043e \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442, \u043a\u0430\u043a \u0432 \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u0434\u0432\u0438\u0436\u0443\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u0438, \u0435\u0441\u043b\u0438 \u043c\u044b \u0431\u0435\u0440\u0451\u043c \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0439 \u0448\u0443\u043c <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi(z)\" alt=\"G_\\phi(z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg\" width=\"46\" height=\"19\" data-width=\"5.732\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 5.732ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u0437\u0430\u0442\u0435\u043c \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u0435\u043c \u0438\u0445 \u043f\u0440\u044f\u043c\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0435\u0439.<\/p>\n<p>\u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u0441\u0442\u0440\u043e\u0438\u043c \u043f\u043e\u043b\u0435 Flow Matching\u2019\u0430, \u043d\u043e \u043d\u0435 \u043d\u0430 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445, \u0430 \u043d\u0430 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/3d7\/52e\/c2e\/3d752ec2ebf523ebd9b3c2bc1b8f2249.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 22. \u041f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 u^\\phi(x,t) \u2014 \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u044e\u0442 \u0448\u0443\u043c x_0 \u0441\u043e \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u043c\u0438 \u043e\u0431\u044a\u0435\u043a\u0442\u0430\u043c\u0438 G_\\phi(z)\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/3d7\/52e\/c2e\/3d752ec2ebf523ebd9b3c2bc1b8f2249.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/3d7\/52e\/c2e\/3d752ec2ebf523ebd9b3c2bc1b8f2249.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 22. \u041f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 u^\\phi(x,t) \u2014 \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u044e\u0442 \u0448\u0443\u043c x_0 \u0441\u043e \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u043c\u0438 \u043e\u0431\u044a\u0435\u043a\u0442\u0430\u043c\u0438 G_\\phi(z)<\/figcaption><\/div>\n<\/figure>\n<h4>\u041b\u043e\u0441\u0441 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438<\/h4>\n<p>\u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0443 \u043d\u0430\u0441 \u0443\u0436\u0435 \u0435\u0441\u0442\u044c \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*(x,t)\" alt=\"u^*(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg\" width=\"57\" height=\"18\" data-width=\"7.159\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.159ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0437\u0430\u0440\u0430\u043d\u0435\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e Flow Matching\u2019\u0430. \u041e\u043d\u043e \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435 \u043e\u0442 \u0448\u0443\u043c\u0430 \u043a \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u043c \u0434\u0430\u043d\u043d\u044b\u043c.<\/p>\n<p>\u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0446\u0435\u043b\u044c \u0443 \u043d\u0430\u0441 \u2014 \u043f\u043e\u0434\u043e\u0431\u0440\u0430\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0435 \u0435\u0433\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"u^\\phi(x,t)\" alt=\"u^\\phi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg\" width=\"58\" height=\"21\" data-width=\"7.312\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 7.312ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u043b\u043e \u0441 \u043f\u043e\u043b\u0435\u043c \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*(x,t)\" alt=\"u^*(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg\" width=\"57\" height=\"18\" data-width=\"7.159\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.159ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0424\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u044d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0442\u0430\u043a:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\min_{G_\\phi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right],\" alt=\"\\min_{G_\\phi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right],\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg\" width=\"398\" height=\"38\" data-width=\"49.693\" data-height=\"4.804\" data-vertical-align=\"-1.837\" style=\"width: 49.693ex; height: 4.804ex; vertical-align: -1.837ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0413\u0434\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_t = (1-t)x_0 + tG_\\phi(z).\" alt=\"\\hat{x}_t = (1-t)x_0 + tG_\\phi(z).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/33\/335\/335d357c2be3e16c71b59608f8d1da30.svg\" width=\"190\" height=\"20\" data-width=\"23.775\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 23.775ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/33\/335\/335d357c2be3e16c71b59608f8d1da30.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/33\/335\/335d357c2be3e16c71b59608f8d1da30.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u043c \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f\u043c \u0438 \u0443\u0447\u0438\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0442\u044c \u043f\u043e\u043b\u044f (\u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438) \u0432 \u0442\u043e\u0447\u043a\u0435. \u041f\u0440\u0438 \u044d\u0442\u043e\u043c \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0435 \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0438 \u043d\u0430\u043c \u043d\u0435 \u043d\u0443\u0436\u043d\u044b, \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u043f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438 Flow Matching\u2019\u0430 \u2014 \u043f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/032\/a94\/283\/032a9428341cdba4582f31c6c1a0906f.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 23. \u041f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435 u^* \u0438 u^\\phi \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0438\u0437 p_z \u0438 p_0; p_1 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u044b \u0434\u043b\u044f \u043d\u0430\u0433\u043b\u044f\u0434\u043d\u043e\u0441\u0442\u0438\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/032\/a94\/283\/032a9428341cdba4582f31c6c1a0906f.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/032\/a94\/283\/032a9428341cdba4582f31c6c1a0906f.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 23. \u041f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435 u^* \u0438 u^\\phi \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0438\u0437 p_z \u0438 p_0; p_1 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u044b \u0434\u043b\u044f \u043d\u0430\u0433\u043b\u044f\u0434\u043d\u043e\u0441\u0442\u0438<\/figcaption><\/div>\n<\/figure>\n<p>\u041c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u0431\u0443\u0447\u0438\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0435\u0433\u043e \u043f\u043e\u043b\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u043b\u043e \u0441 \u043f\u043e\u043b\u0435\u043c \u043d\u0430 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445. \u0415\u0449\u0435 \u043c\u044b \u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_0\" alt=\"\\hat{x}_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d3\/d3a\/d3ac95831ab159e2c421c58f6b46661d.svg\" width=\"18\" height=\"19\" data-width=\"2.282\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.282ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d3\/d3a\/d3ac95831ab159e2c421c58f6b46661d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d3\/d3a\/d3ac95831ab159e2c421c58f6b46661d.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 (\u044d\u0442\u043e \u043f\u0440\u043e\u0441\u0442\u043e \u0433\u0430\u0443\u0441\u0441\u0438\u0430\u043d\u044b). \u0422\u043e\u0433\u0434\u0430 \u0441\u043e\u0432\u043f\u0430\u0434\u0443\u0442 \u0438 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438, \u043f\u043e \u043a\u043e\u0442\u043e\u0440\u044b\u043c \u043c\u044b \u0434\u0432\u0438\u0436\u0435\u043c\u0441\u044f, \u0438 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u043f\u043e \u043d\u0438\u043c \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f (\u043e\u0431\u0441\u0443\u0434\u0438\u043b\u0438 \u0432 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u043c \u0432\u044b\u0432\u043e\u0434\u0435 Flow Matching).<\/p>\n<p>\u041d\u043e \u044d\u0442\u043e \u043f\u043e\u043a\u0430 \u0438\u0434\u0435\u0430\u043b\u044c\u043d\u0430\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0446\u0435\u043b\u044c. \u041d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u^\\phi(x,t)\" alt=\"u^\\phi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg\" width=\"58\" height=\"21\" data-width=\"7.312\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 7.312ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e \u044f\u0432\u043d\u043e, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043e\u043d\u043e \u0441\u0430\u043c\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u043c \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u043f\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0442\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u0438\u0434\u0443\u043c\u0430\u0442\u044c, \u043a\u0430\u043a \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u044c \u0446\u0435\u043b\u044c \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0443\u0434\u043e\u0431\u043d\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f! \ud83d\ude09<\/p>\n<h4>\u041a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u043b\u043e\u0441\u0441 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 (\u0434\u0435\u043b\u0430\u0442\u044c tractable)<\/h4>\n<p>\u0412 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u0438\u0434\u0435\u0430\u043b\u044c\u043d\u0443\u044e \u0446\u0435\u043b\u044c \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\min_{G_\\phi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right],\" alt=\"\\min_{G_\\phi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right],\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg\" width=\"398\" height=\"38\" data-width=\"49.693\" data-height=\"4.804\" data-vertical-align=\"-1.837\" style=\"width: 49.693ex; height: 4.804ex; vertical-align: -1.837ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0413\u0434\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1,\" alt=\"\\hat{x}_1 = G_\\phi(z), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9b8\/9b86188b6545a897c6cf31543b4c84ce.svg\" width=\"295\" height=\"20\" data-width=\"36.887\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 36.887ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9b8\/9b86188b6545a897c6cf31543b4c84ce.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9b8\/9b86188b6545a897c6cf31543b4c84ce.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0410 \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u043a \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^\\phi(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\hat{x}_1 - x_0 \\mid \\hat{x}_t = x \\right].\" alt=\"u^\\phi(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\hat{x}_1 - x_0 \\mid \\hat{x}_t = x \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e7d\/e7da84ba68ca0aa4ec9b72a0b72b1702.svg\" width=\"380\" height=\"23\" data-width=\"47.54\" data-height=\"2.907\" data-vertical-align=\"-0.888\" style=\"width: 47.54ex; height: 2.907ex; vertical-align: -0.888ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e7d\/e7da84ba68ca0aa4ec9b72a0b72b1702.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e7d\/e7da84ba68ca0aa4ec9b72a0b72b1702.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"u^\\phi(x,t)\" alt=\"u^\\phi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg\" width=\"58\" height=\"21\" data-width=\"7.312\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 7.312ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0435\u043b\u044c\u0437\u044f \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e. \u042d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043f\u043e \u0432\u0441\u0435\u043c \u043f\u0430\u0440\u0430\u043c <img decoding=\"async\" class=\"formula inline\" source=\"(x_0,z)\" alt=\"(x_0,z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afa\/afa910e6a7af91b3309438ff9c670a68.svg\" width=\"49\" height=\"18\" data-width=\"6.1\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.1ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afa\/afa910e6a7af91b3309438ff9c670a68.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afa\/afa910e6a7af91b3309438ff9c670a68.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043b\u0438, \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e, <img decoding=\"async\" class=\"formula inline\" source=\"(x_0, \\hat{x}_1)\" alt=\"(x_0, \\hat{x}_1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/91\/91e\/91e6f2021b66a0cd63980a3530497ce9.svg\" width=\"59\" height=\"19\" data-width=\"7.33\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.33ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/91\/91e\/91e6f2021b66a0cd63980a3530497ce9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/91\/91e\/91e6f2021b66a0cd63980a3530497ce9.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"12\" height=\"12\" data-width=\"1.294\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.294ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430\u043c \u043d\u0443\u0436\u0435\u043d \u0441\u043f\u043e\u0441\u043e\u0431 \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u044c \u044d\u0442\u043e \u043f\u043e\u043b\u0435.<\/p>\n<p>\u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u0432\u0435\u0434\u0451\u043c \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u0443\u044e Flow Matching-\u043c\u043e\u0434\u0435\u043b\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(x,t)\" alt=\"u_\\psi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg\" width=\"59\" height=\"19\" data-width=\"7.4\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 7.4ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0415\u0451 \u0437\u0430\u0434\u0430\u0447\u0430 \u2014 \u0443\u0447\u0438\u0442\u044c\u0441\u044f \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0442\u044c \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1 - x_0\" alt=\"\\hat{x}_1 - x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0d\/0d7\/0d7396adaeef4a762505d7bc5a1cdfa2.svg\" width=\"59\" height=\"19\" data-width=\"7.329\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.329ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0d\/0d7\/0d7396adaeef4a762505d7bc5a1cdfa2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0d\/0d7\/0d7396adaeef4a762505d7bc5a1cdfa2.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0447\u0442\u043e\u0431\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u044d\u0442\u0443 \u043c\u043e\u0434\u0435\u043b\u044c \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043b\u043e\u0441\u0441\u0430.<\/p>\n<p>\u0422\u043e \u0435\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u0431\u0443\u0447\u0430\u0435\u0442\u0441\u044f, \u043a\u0430\u043a \u0438 Flow Matching-\u043c\u043e\u0434\u0435\u043b\u044c, \u0442\u043e\u043b\u044c\u043a\u043e \u0432\u043c\u0435\u0441\u0442\u043e \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 <img decoding=\"async\" class=\"formula inline\" source=\"x_1\\sim p_{\\text{data}}\" alt=\"x_1\\sim p_{\\text{data}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a65\/a65cc2fca8a72f42e914c08bc2ccca69.svg\" width=\"78\" height=\"18\" data-width=\"9.736\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 9.736ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a65\/a65cc2fca8a72f42e914c08bc2ccca69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a65\/a65cc2fca8a72f42e914c08bc2ccca69.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u043e\u0431\u044a\u0435\u043a\u0442\u044b:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z).\" alt=\"\\hat{x}_1 = G_\\phi(z).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg\" width=\"93\" height=\"20\" data-width=\"11.66\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 11.66ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0440\u0438 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u043e\u0434\u0435\u043b\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u0443\u0447\u0430\u0442\u044c \u043e\u0431\u044b\u0447\u043d\u043e\u0439 MSE-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0435\u0439:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\min_{u_\\psi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t) - (\\hat{x}_1-x_0) \\right\\|_2^2 \\right].\" alt=\"\\min_{u_\\psi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t) - (\\hat{x}_1-x_0) \\right\\|_2^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6ad\/6ad90f42ac6323caff7fb4575e0f2131.svg\" width=\"408\" height=\"37\" data-width=\"50.947\" data-height=\"4.656\" data-vertical-align=\"-1.763\" style=\"width: 50.947ex; height: 4.656ex; vertical-align: -1.763ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6ad\/6ad90f42ac6323caff7fb4575e0f2131.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6ad\/6ad90f42ac6323caff7fb4575e0f2131.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041a\u0430\u043a \u0438 \u0440\u0430\u043d\u044c\u0448\u0435, \u043c\u0438\u043d\u0438\u043c\u0443\u043c MSE \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u043c\u0443 \u0441\u0440\u0435\u0434\u043d\u0435\u043c\u0443, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432 \u043e\u043f\u0442\u0438\u043c\u0443\u043c\u0435 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u_\\psi(x,t) \\approx u^\\phi(x,t).\" alt=\"u_\\psi(x,t) \\approx u^\\phi(x,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg\" width=\"147\" height=\"22\" data-width=\"18.359\" data-height=\"2.712\" data-vertical-align=\"-0.79\" style=\"width: 18.359ex; height: 2.712ex; vertical-align: -0.79ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(x,t)\" alt=\"u_\\psi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg\" width=\"59\" height=\"19\" data-width=\"7.4\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 7.4ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u043d\u0430\u0437\u044b\u0432\u0430\u0442\u044c <strong>\u0444\u0435\u0439\u043a-\u043c\u043e\u0434\u0435\u043b\u044c\u044e<\/strong> \u2014 \u043e\u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0430 \u043d\u0430 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 (\u0444\u0435\u0439\u043a\u043e\u0432\u044b\u0445) \u0434\u0430\u043d\u043d\u044b\u0445.<\/p>\n<p>\ud83d\udca1 \u0417\u0434\u0435\u0441\u044c \u0432\u0430\u0436\u043d\u043e \u043d\u0435 \u043f\u0435\u0440\u0435\u043f\u0443\u0442\u0430\u0442\u044c \u0442\u0440\u0438 \u0440\u0430\u0437\u043d\u044b\u0445 \u043f\u043e\u043b\u044f:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^*(x,t)\" alt=\"u^*(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg\" width=\"57\" height=\"18\" data-width=\"7.159\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.159ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u2014 \u044d\u0442\u043e \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0438\u0437 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 (\u043c\u044b \u0432\u044b\u0443\u0447\u0438\u043b\u0438 \u0435\u0433\u043e \u0437\u0430\u0440\u0430\u043d\u0435\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e Flow Matching-\u043b\u043e\u0441\u0441\u0430);<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^\\phi(x,t)\" alt=\"u^\\phi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg\" width=\"58\" height=\"21\" data-width=\"7.312\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 7.312ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u2014 \u0438\u0441\u0442\u0438\u043d\u043d\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 (\u0435\u0433\u043e \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043c\u0430\u0442\u043e\u0436 \u043f\u043e \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u043c\u0443 \u0447\u0438\u0441\u043b\u0443 \u0441\u0435\u043c\u043f\u043b\u043e\u0432);<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u_\\psi(x,t)\" alt=\"u_\\psi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg\" width=\"59\" height=\"19\" data-width=\"7.4\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 7.4ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u2014 \u043e\u0431\u0443\u0447\u0430\u0435\u043c\u0430\u044f \u0444\u0435\u0439\u043a-\u043c\u043e\u0434\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"u^\\phi(x,t)\" alt=\"u^\\phi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg\" width=\"58\" height=\"21\" data-width=\"7.312\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 7.312ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3da87145575ab0dd7c42cccae08b2a79.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0412\u044b\u043f\u0438\u0448\u0435\u043c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e \u0442\u0435\u043a\u0443\u0449\u0438\u0435 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f. \u041a \u043d\u0438\u043c \u043c\u043e\u0436\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0442\u044c\u0441\u044f \u043f\u0440\u0438 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \ud83d\ude07<\/p>\n<div>\n<div class=\"table\">\n<table>\n<tbody>\n<tr>\n<th>\n<p align=\"left\"><strong>\u041e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435<\/strong><\/p>\n<\/th>\n<th>\n<p align=\"left\"><strong>\u0421\u043c\u044b\u0441\u043b<\/strong><\/p>\n<\/th>\n<\/tr>\n<tr>\n<td>\n<p align=\"left\"><img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/td>\n<td>\n<p align=\"left\">\u0448\u0443\u043c \u0432 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width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442 \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u2014 \u043c\u043e\u0436\u043d\u043e \u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0442\u044c \u0435\u0433\u043e \u0441 \u043f\u043e\u043b\u0435\u043c \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u0445\u043e\u0442\u0438\u043c, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0441\u0442\u0430\u043b\u043e \u0431\u043b\u0438\u0436\u0435 \u043a \u043f\u043e\u043b\u044e \u0443\u0447\u0438\u0442\u0435\u043b\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0434\u043e\u043b\u0436\u0435\u043d \u043c\u0435\u043d\u044f\u0442\u044c \u0441\u0432\u043e\u0438 \u0432\u044b\u0445\u043e\u0434\u044b \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u043e\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043a <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi(z)\" alt=\"G_\\phi(z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg\" width=\"46\" height=\"19\" data-width=\"5.732\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 5.732ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043c\u0435\u043b\u0438 \u0442\u0430\u043a\u043e\u0435 \u0436\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439, \u043a\u0430\u043a \u0443 \u0443\u0447\u0438\u0442\u0435\u043b\u044f.<\/p>\n<p>\u0422\u0443\u0442 \u0438 \u043f\u043e\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0438\u0433\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043f\u0435\u0440\u0432\u044b\u0439 \u0443\u0447\u0438\u0442 \u043f\u043e\u043b\u0435, \u0441\u043e\u0437\u0434\u0430\u043d\u043d\u043e\u0435 \u0432\u0442\u043e\u0440\u044b\u043c, \u0430 \u0432\u0442\u043e\u0440\u043e\u0439 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0432\u044b\u0443\u0447\u0438\u043b \u043f\u0435\u0440\u0432\u044b\u0439. \u041c\u043e\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0438\u0433\u0440\u0443 \u043c\u0435\u0436\u0434\u0443 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u043e\u043c <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u043f\u043e\u043b\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\min_{G_\\phi}\\max_{u_\\psi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - (\\hat{x}_1-x_0) \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t) - (\\hat{x}_1-x_0) \\right\\|_2^2 \\right].\" alt=\"\\min_{G_\\phi}\\max_{u_\\psi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - (\\hat{x}_1-x_0) \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t) - (\\hat{x}_1-x_0) \\right\\|_2^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/16\/16d\/16d57d1decb32a70076f7c5b3826fe85.svg\" width=\"653\" height=\"38\" data-width=\"81.583\" data-height=\"4.804\" data-vertical-align=\"-1.837\" style=\"width: 81.583ex; height: 4.804ex; vertical-align: -1.837ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/16\/16d\/16d57d1decb32a70076f7c5b3826fe85.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/16\/16d\/16d57d1decb32a70076f7c5b3826fe85.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/081\/ea5\/525\/081ea55257a1282c706db3e5f43081ad.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 24. \u0421\u0445\u0435\u043c\u0430 \u043c\u0435\u0442\u043e\u0434\u0430. \u0421\u043f\u0440\u0430\u0432\u0430 \u0432 \u043b\u043e\u0441\u0441\u0435 \u2014 \u043d\u0435 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c u \u0438 v, \u0430 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c x_t + (1 - t) u \u0438 x_1 \u0434\u043b\u044f \u043d\u0430\u0433\u043b\u044f\u0434\u043d\u043e\u0441\u0442\u0438 (\u0442\u0430\u043a \u043a\u0430\u043a x_1 = x_t + (1 - t) (x_1 - x_0), \u0442\u043e \u0441 \u0442\u043e\u0447\u043d\u043e\u0441\u0442\u044c\u044e \u0434\u043e \u0432\u0435\u0441\u0430 \u044d\u0442\u043e \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435)\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/081\/ea5\/525\/081ea55257a1282c706db3e5f43081ad.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/081\/ea5\/525\/081ea55257a1282c706db3e5f43081ad.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 24. \u0421\u0445\u0435\u043c\u0430 \u043c\u0435\u0442\u043e\u0434\u0430. \u0421\u043f\u0440\u0430\u0432\u0430 \u0432 \u043b\u043e\u0441\u0441\u0435 \u2014 \u043d\u0435 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c u \u0438 v, \u0430 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c x_t + (1 &#8212; t) u \u0438 x_1 \u0434\u043b\u044f \u043d\u0430\u0433\u043b\u044f\u0434\u043d\u043e\u0441\u0442\u0438 (\u0442\u0430\u043a \u043a\u0430\u043a x_1 = x_t + (1 &#8212; t) (x_1 &#8212; x_0), \u0442\u043e \u0441 \u0442\u043e\u0447\u043d\u043e\u0441\u0442\u044c\u044e \u0434\u043e \u0432\u0435\u0441\u0430 \u044d\u0442\u043e \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435)<\/figcaption><\/div>\n<\/figure>\n<p>\u0422\u043e \u0435\u0441\u0442\u044c \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0444\u0435\u0439\u043a-\u043c\u043e\u0434\u0435\u043b\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u0430\u043a\u0441\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0432\u043d\u0443\u0442\u0440\u0438, \u0438 \u043a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u043f\u0442\u0438\u043c\u0443\u043c, \u043c\u044b \u0434\u0435\u043b\u0430\u0435\u043c \u043d\u0435\u0431\u043e\u043b\u044c\u0448\u043e\u0439 \u0448\u0430\u0433 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0422\u043e \u0435\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e\u043b\u0436\u0435\u043d \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u041c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0432 \u043d\u043e\u0432\u043e\u0439 \u0438\u0433\u0440\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u0430\u043a\u0436\u0435 \u0443\u0447\u0438\u0442\u0441\u044f \u043f\u043e \u043b\u043e\u0441\u0441\u0443 Flow Matching\u2019\u0430 \u043d\u0430 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\min_{u_\\psi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t) - (\\hat{x}_1-x_0) \\right\\|_2^2 \\right].\" alt=\"\\min_{u_\\psi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t) - (\\hat{x}_1-x_0) \\right\\|_2^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6ad\/6ad90f42ac6323caff7fb4575e0f2131.svg\" width=\"408\" height=\"37\" data-width=\"50.947\" data-height=\"4.656\" data-vertical-align=\"-1.763\" style=\"width: 50.947ex; height: 4.656ex; vertical-align: -1.763ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6ad\/6ad90f42ac6323caff7fb4575e0f2131.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6a\/6ad\/6ad90f42ac6323caff7fb4575e0f2131.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043f\u0435\u0440\u0432\u044b\u0439 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u043d\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\max -x = \\min x\" alt=\"\\max -x = \\min x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/395\/3955d82f8955c4fc0e093b6433149d2a.svg\" width=\"129\" height=\"18\" data-width=\"16.102\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 16.102ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/395\/3955d82f8955c4fc0e093b6433149d2a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/395\/3955d82f8955c4fc0e093b6433149d2a.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0412 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0439 \u0438\u0433\u0440\u0435 \u043f\u0435\u0440\u0432\u043e\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 \u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u0442 \u0442\u0435\u043a\u0443\u0449\u0443\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0441 \u043f\u043e\u043b\u0435\u043c \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0412\u0442\u043e\u0440\u043e\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 \u0432\u044b\u0447\u0438\u0442\u0430\u0435\u0442 \u043e\u0448\u0438\u0431\u043a\u0443 \u043b\u0443\u0447\u0448\u0435\u0433\u043e \u043f\u043e\u043b\u044f, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u044b\u0443\u0447\u0435\u043d\u043e \u043d\u0430 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f\u0445 \u0441\u0430\u043c\u043e\u0433\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430.<\/p>\n<p>\u0418\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e \u044d\u0442\u043e \u0443\u0431\u0438\u0440\u0430\u0435\u0442 \u0438\u0437 \u043b\u043e\u0441\u0441\u0430 \u0442\u0443 \u0447\u0430\u0441\u0442\u044c \u043e\u0448\u0438\u0431\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u0440\u0430\u0437\u0431\u0440\u043e\u0441\u043e\u043c \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u0438\u0437 \u0440\u0430\u0437\u043d\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439, \u0438 \u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u043f\u043e\u043b\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0438 \u0443\u0447\u0438\u0442\u0435\u043b\u044f. \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0443\u0437\u043d\u0430\u0435\u043c, \u043f\u043e\u0447\u0435\u043c\u0443 \u044d\u0442\u043e \u0442\u0430\u043a \u2014 \u0441\u043c. \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0434\u0432\u0430 \u0441\u043a\u0440\u044b\u0442\u044b\u0445 \u0431\u043b\u043e\u043a\u0430.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/594\/fb3\/b64\/594fb3b647b4a08a86b581fa722eeb0c.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 25. \u0421\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u044b\u043c \u043b\u043e\u0441\u0441\u043e\u043c \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f u^*, \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 u^\\phi \u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f u_\\psi, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u044c \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043f\u043e\u0442\u043e\u043a \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043a \u0443\u0447\u0438\u0442\u0435\u043b\u044e\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/594\/fb3\/b64\/594fb3b647b4a08a86b581fa722eeb0c.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/594\/fb3\/b64\/594fb3b647b4a08a86b581fa722eeb0c.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 25. \u0421\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u044b\u043c \u043b\u043e\u0441\u0441\u043e\u043c \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f u^*, \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 u^\\phi \u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f u_\\psi, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u044c \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043f\u043e\u0442\u043e\u043a \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043a \u0443\u0447\u0438\u0442\u0435\u043b\u044e<\/figcaption><\/div>\n<\/figure>\n<details class=\"spoiler\">\n<summary>\u0421\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u043e\u0439 \u0446\u0435\u043b\u044c\u044e \u0441\u0440\u0435\u0434\u043d\u0438\u0445 \u043f\u043e\u043b\u0435\u0439<\/summary>\n<div class=\"spoiler__content\">\n<p>\u0415\u0441\u043b\u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u0444\u0435\u0439\u043a-\u043c\u043e\u0434\u0435\u043b\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0434\u0435\u0430\u043b\u044c\u043d\u043e \u0432\u044b\u0443\u0447\u0438\u043b\u0430 \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u2014 \u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u0430\u044f \u0446\u0435\u043b\u044c \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u00ab\u0432\u044b\u0443\u0447\u0438\u0432\u0430\u043d\u0438\u0435\u00bb:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^\\phi(x,t) \\approx u^*(x,t).\" alt=\"u^\\phi(x,t) \\approx u^*(x,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b40\/b409d8717b9fd52d7037797e3074571c.svg\" width=\"145\" height=\"21\" data-width=\"18.117\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 18.117ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b40\/b409d8717b9fd52d7037797e3074571c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b40\/b409d8717b9fd52d7037797e3074571c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u0430\u0444\u0438\u043a\u0441\u0438\u0440\u0443\u0435\u043c \u0442\u043e\u0447\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0432\u0440\u0435\u043c\u044f <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041e\u0431\u043e\u0437\u043d\u0430\u0447\u0438\u043c \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0447\u0435\u0440\u0435\u0437:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"v = \\hat{x}_1 - x_0.\" alt=\"v = \\hat{x}_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg\" width=\"97\" height=\"19\" data-width=\"12.073\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 12.073ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e\u0433\u0434\u0430 \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u2014 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u044d\u0442\u043e\u0439 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^\\phi(\\hat{x}_t,t) = \\mathbb{E}_{x_0,z} \\left[ v \\mid \\hat{x}_t,t \\right].\" alt=\"u^\\phi(\\hat{x}_t,t) = \\mathbb{E}_{x_0,z} \\left[ v \\mid \\hat{x}_t,t \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a6\/3a63dfef3842303cdc546c9d90d35aa1.svg\" width=\"203\" height=\"23\" data-width=\"25.352\" data-height=\"2.835\" data-vertical-align=\"-0.852\" style=\"width: 25.352ex; height: 2.835ex; vertical-align: -0.852ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a6\/3a63dfef3842303cdc546c9d90d35aa1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a6\/3a63dfef3842303cdc546c9d90d35aa1.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0414\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"a(\\hat{x}_t,t)\" alt=\"a(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fbb\/fbbfde042d33edfaffecd8a0c4a117b3.svg\" width=\"55\" height=\"19\" data-width=\"6.839\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 6.839ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fbb\/fbbfde042d33edfaffecd8a0c4a117b3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fbb\/fbbfde042d33edfaffecd8a0c4a117b3.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432\u0435\u0440\u043d\u043e \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0435 MSE (\u043c\u044b \u0443\u0436\u0435 \u0434\u0435\u043b\u0430\u043b\u0438 \u044d\u0442\u043e, \u043a\u043e\u0433\u0434\u0430 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u043b\u0438, \u043f\u043e\u0447\u0435\u043c\u0443 \u043f\u0440\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0438 MSE \u043c\u044b \u0432\u044b\u0443\u0447\u0438\u0432\u0430\u0435\u043c \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435):<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathbb{E}_{x_0,z} \\left[ \\left\\| a(\\hat{x}_t,t)-v \\right\\|_2^2 \\mid \\hat{x}_t,t \\right] = \\left\\| a(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 + \\operatorname{tr} \\operatorname{Cov}_{x_0,z} \\left( v \\mid \\hat{x}_t,t \\right).\" alt=\"\\mathbb{E}_{x_0,z} \\left[ \\left\\| a(\\hat{x}_t,t)-v \\right\\|_2^2 \\mid \\hat{x}_t,t \\right] = \\left\\| a(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 + \\operatorname{tr} \\operatorname{Cov}_{x_0,z} \\left( v \\mid \\hat{x}_t,t \\right).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4a\/e4ad1380736bebac5fabfed5bfc4da0b.svg\" width=\"584\" height=\"33\" data-width=\"72.992\" data-height=\"4.07\" data-vertical-align=\"-1.469\" style=\"width: 72.992ex; height: 4.07ex; vertical-align: -1.469ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4a\/e4ad1380736bebac5fabfed5bfc4da0b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4a\/e4ad1380736bebac5fabfed5bfc4da0b.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0432\u043c\u0435\u0441\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"a\" alt=\"a\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg\" width=\"12\" height=\"12\" data-width=\"1.197\" data-height=\"1.02\" data-vertical-align=\"-0.023\" style=\"width: 1.197ex; height: 1.02ex; vertical-align: -0.023ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} &amp; \\mathbb{E}_{x_0,z} \\left[ \\left\\| u^*(\\hat{x}_t,t)-v \\right\\|_2^2 \\mid \\hat{x}_t,t \\right] \\\\ &amp;= \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 + \\operatorname{tr} \\operatorname{Cov}_{x_0,z} \\left( v \\mid \\hat{x}_t,t \\right). \\end{aligned}\" alt=\"\\begin{aligned} &amp; \\mathbb{E}_{x_0,z} \\left[ \\left\\| u^*(\\hat{x}_t,t)-v \\right\\|_2^2 \\mid \\hat{x}_t,t \\right] \\\\ &amp;= \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 + \\operatorname{tr} \\operatorname{Cov}_{x_0,z} \\left( v \\mid \\hat{x}_t,t \\right). \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8b8b68a74d6809d2c40c803c8d4fa1.svg\" width=\"377\" height=\"66\" data-width=\"47.091\" data-height=\"8.235\" data-vertical-align=\"-3.552\" style=\"width: 47.091ex; height: 8.235ex; vertical-align: -3.552ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8b8b68a74d6809d2c40c803c8d4fa1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6f8\/6f8b8b68a74d6809d2c40c803c8d4fa1.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u2014 \u0432\u043c\u0435\u0441\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"a\" alt=\"a\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg\" width=\"12\" height=\"12\" data-width=\"1.197\" data-height=\"1.02\" data-vertical-align=\"-0.023\" style=\"width: 1.197ex; height: 1.02ex; vertical-align: -0.023ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0434\u0435\u0430\u043b\u044c\u043d\u043e\u0435 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435. \u0415\u0441\u043b\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u0431\u0443\u0447\u0435\u043d\u043e \u0438\u0434\u0435\u0430\u043b\u044c\u043d\u043e:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u_\\psi(\\hat{x}_t,t) = u^\\phi(\\hat{x}_t,t).\" alt=\"u_\\psi(\\hat{x}_t,t) = u^\\phi(\\hat{x}_t,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/410\/4104b219742c10f708c075fa7d640cf5.svg\" width=\"159\" height=\"22\" data-width=\"19.89\" data-height=\"2.712\" data-vertical-align=\"-0.79\" style=\"width: 19.89ex; height: 2.712ex; vertical-align: -0.79ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/410\/4104b219742c10f708c075fa7d640cf5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/410\/4104b219742c10f708c075fa7d640cf5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u044d\u0442\u043e\u043c\u0443:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} &amp; \\mathbb{E}_{x_0,z} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t)-v \\right\\|_2^2 \\mid \\hat{x}_t,t \\right] \\\\ &amp;= \\operatorname{tr} \\operatorname{Cov}_{x_0,z} \\left( v \\mid \\hat{x}_t,t \\right). \\end{aligned}\" alt=\"\\begin{aligned} &amp; \\mathbb{E}_{x_0,z} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t)-v \\right\\|_2^2 \\mid \\hat{x}_t,t \\right] \\\\ &amp;= \\operatorname{tr} \\operatorname{Cov}_{x_0,z} \\left( v \\mid \\hat{x}_t,t \\right). \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f2\/f20\/f20ac3b1bac88a9567f243ab97e38c20.svg\" width=\"226\" height=\"60\" data-width=\"28.312\" data-height=\"7.462\" data-vertical-align=\"-3.165\" style=\"width: 28.312ex; height: 7.462ex; vertical-align: -3.165ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f2\/f20\/f20ac3b1bac88a9567f243ab97e38c20.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f2\/f20\/f20ac3b1bac88a9567f243ab97e38c20.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412\u044b\u0447\u0442\u0435\u043c \u0432\u0442\u043e\u0440\u043e\u0435 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0438\u0437 \u043f\u0435\u0440\u0432\u043e\u0433\u043e. \u0414\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u043e\u043d\u043d\u044b\u0435 \u0447\u043b\u0435\u043d\u044b \u0441\u043e\u043a\u0440\u0430\u0442\u044f\u0442\u0441\u044f:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} &amp; \\mathbb{E}_{x_0,z} \\left[ \\left\\| u^*(\\hat{x}_t,t)-v \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t)-v \\right\\|_2^2 \\mid \\hat{x}_t,t \\right] \\\\ &amp;= \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2. \\end{aligned}\" alt=\"\\begin{aligned} &amp; \\mathbb{E}_{x_0,z} \\left[ \\left\\| u^*(\\hat{x}_t,t)-v \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t)-v \\right\\|_2^2 \\mid \\hat{x}_t,t \\right] \\\\ &amp;= \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2. \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/43\/435\/435cc7e3dd754eadfc390e47690d8c14.svg\" width=\"371\" height=\"66\" data-width=\"46.368\" data-height=\"8.235\" data-vertical-align=\"-3.552\" style=\"width: 46.368ex; height: 8.235ex; vertical-align: -3.552ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/43\/435\/435cc7e3dd754eadfc390e47690d8c14.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/43\/435\/435cc7e3dd754eadfc390e47690d8c14.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0432\u043e\u0437\u044c\u043c\u0451\u043c \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435 \u043f\u043e \u0432\u0441\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"z\" alt=\"z\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg\" width=\"12\" height=\"12\" data-width=\"1.052\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.052ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} &amp; \\mathbb{E}_{t,\\hat{x}_t} \\mathbb{E}_{x_0,z | t, \\hat{x}_t} \\left[ \\left\\| u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 \\right] \\\\ &amp;= \\mathbb{E}_{t,\\hat{x}_t} \\mathbb{E}_{x_0,z | t, \\hat{x}_t} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right] \\\\ &amp;= \\mathbb{E}_{t,\\,x_0,z} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right]. \\end{aligned}\" alt=\"\\begin{aligned} &amp; \\mathbb{E}_{t,\\hat{x}_t} \\mathbb{E}_{x_0,z | t, \\hat{x}_t} \\left[ \\left\\| u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 \\right] \\\\ &amp;= \\mathbb{E}_{t,\\hat{x}_t} \\mathbb{E}_{x_0,z | t, \\hat{x}_t} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right] \\\\ &amp;= \\mathbb{E}_{t,\\,x_0,z} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right]. \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e14\/e14a88edb6794601b7ede5bf48c9513c.svg\" width=\"509\" height=\"109\" data-width=\"63.683\" data-height=\"13.568\" data-vertical-align=\"-6.218\" style=\"width: 63.683ex; height: 13.568ex; vertical-align: -6.218ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e14\/e14a88edb6794601b7ede5bf48c9513c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e14\/e14a88edb6794601b7ede5bf48c9513c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0442\u0430\u043a\u0430\u044f \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c \u0434\u0432\u0443\u0445 MSE-\u043e\u0448\u0438\u0431\u043e\u043a \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0443\u0434\u043e\u0431\u043d\u044b\u043c \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u043c \u043e\u0431\u0443\u0447\u0430\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440. \u041e\u043d\u0430 \u0437\u0430\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u043a\u0430\u0436\u0434\u0443\u044e \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u0443\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1-x_0\" alt=\"\\hat{x}_1-x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/eb\/ebd\/ebd85e138ac6e0e934bba41f60098f09.svg\" width=\"59\" height=\"19\" data-width=\"7.329\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.329ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/eb\/ebd\/ebd85e138ac6e0e934bba41f60098f09.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/eb\/ebd\/ebd85e138ac6e0e934bba41f60098f09.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0442\u044c \u043d\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u0435 \u0441\u0440\u0435\u0434\u043d\u0438\u0435 \u043f\u043e\u043b\u044f:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^\\phi(x,t) \\approx u^*(x,t).\" alt=\"u^\\phi(x,t) \\approx u^*(x,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b40\/b409d8717b9fd52d7037797e3074571c.svg\" width=\"145\" height=\"21\" data-width=\"18.117\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 18.117ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b40\/b409d8717b9fd52d7037797e3074571c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b40\/b409d8717b9fd52d7037797e3074571c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u042d\u0442\u043e \u0432\u0430\u0436\u043d\u043e: \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0440\u0430\u0437\u043d\u044b\u043c\u0438, \u043d\u043e \u0438\u0445 \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043f\u043e\u0442\u043e\u043a \u0434\u043e\u043b\u0436\u0435\u043d \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0442\u044c \u0441 \u043f\u043e\u0442\u043e\u043a\u043e\u043c \u0443\u0447\u0438\u0442\u0435\u043b\u044f.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/69b\/005\/493\/69b0054931db83422c7e2ed804a34a2c.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 26. \u041c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u0430\u044f \u0446\u0435\u043b\u044c \u0443\u0431\u0438\u0440\u0430\u0435\u0442 \u0440\u0430\u0437\u0431\u0440\u043e\u0441 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0438 \u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441\u0440\u0435\u0434\u043d\u0438\u0445 \u043f\u043e\u043b\u0435\u0439\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/69b\/005\/493\/69b0054931db83422c7e2ed804a34a2c.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/69b\/005\/493\/69b0054931db83422c7e2ed804a34a2c.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 26. \u041c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u0430\u044f \u0446\u0435\u043b\u044c \u0443\u0431\u0438\u0440\u0430\u0435\u0442 \u0440\u0430\u0437\u0431\u0440\u043e\u0441 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0438 \u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441\u0440\u0435\u0434\u043d\u0438\u0445 \u043f\u043e\u043b\u0435\u0439<\/figcaption><\/div>\n<\/figure>\n<\/div>\n<\/details>\n<details class=\"spoiler\">\n<summary>\u041b\u0438\u043d\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u044f<\/summary>\n<div class=\"spoiler__content\">\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0442\u043e\u0442 \u0436\u0435 \u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u044b\u0439 \u043b\u043e\u0441\u0441. \u042d\u0442\u043e\u0442 \u0432\u044b\u0432\u043e\u0434 \u043e\u0441\u043d\u043e\u0432\u0430\u043d \u043d\u0430 <strong>\u043f\u0440\u0438\u0451\u043c\u0435 \u043b\u0438\u043d\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u0438<\/strong> (<em>linearization trick<\/em>), \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0432 \u043d\u0430\u0448\u0435\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 <a href=\"https:\/\/arxiv.org\/abs\/2509.22459\" rel=\"noopener nofollow\">RealUID<\/a>.<\/p>\n<p>\u041d\u0430\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0438\u0434\u0435\u0430\u043b\u044c\u043d\u0430\u044f \u0446\u0435\u043b\u044c \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0441\u043e\u0433\u043b\u0430\u0441\u043e\u0432\u0430\u043d\u0438\u0438 \u0434\u0432\u0443\u0445 \u0441\u0440\u0435\u0434\u043d\u0438\u0445 \u043f\u043e\u043b\u0435\u0439:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\min_{G_\\phi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right],\" alt=\"\\min_{G_\\phi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right],\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg\" width=\"398\" height=\"38\" data-width=\"49.693\" data-height=\"4.804\" data-vertical-align=\"-1.837\" style=\"width: 49.693ex; height: 4.804ex; vertical-align: -1.837ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0413\u0434\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1,\" alt=\"\\hat{x}_1 = G_\\phi(z), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9b8\/9b86188b6545a897c6cf31543b4c84ce.svg\" width=\"295\" height=\"20\" data-width=\"36.887\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 36.887ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9b8\/9b86188b6545a897c6cf31543b4c84ce.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9b8\/9b86188b6545a897c6cf31543b4c84ce.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0410 \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u043e:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^\\phi(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\hat{x}_1-x_0 \\mid \\hat{x}_t=x \\right].\" alt=\"u^\\phi(x,t) = \\mathbb{E}_{x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\hat{x}_1-x_0 \\mid \\hat{x}_t=x \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e16\/e16f9f495840bd4eba4c105ff5dd9d00.svg\" width=\"380\" height=\"23\" data-width=\"47.54\" data-height=\"2.907\" data-vertical-align=\"-0.888\" style=\"width: 47.54ex; height: 2.907ex; vertical-align: -0.888ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e16\/e16f9f495840bd4eba4c105ff5dd9d00.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e16\/e16f9f495840bd4eba4c105ff5dd9d00.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u0437\u0434\u0435\u0441\u044c \u0441\u0442\u043e\u0438\u0442 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c \u0441 \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u043c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u^\\phi\" alt=\"u^\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/06\/068\/068b42ae9de0931089634fecf0864084.svg\" width=\"19\" height=\"21\" data-width=\"2.435\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 2.435ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/06\/068\/068b42ae9de0931089634fecf0864084.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/06\/068\/068b42ae9de0931089634fecf0864084.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041d\u0430\u043f\u0440\u044f\u043c\u0443\u044e \u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0442\u0430\u043a\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043d\u0435\u043b\u044c\u0437\u044f \u2014 \u043d\u0443\u0436\u043d\u043e \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0440\u0430\u0437 \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c.<\/p>\n<p>\u0417\u0430\u043f\u0438\u0448\u0435\u043c \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c \u043f\u043e\u043b\u0435\u0439 \u0432 \u0434\u0440\u0443\u0433\u043e\u0439 \u0444\u043e\u0440\u043c\u0435. \u0422\u0430\u043a \u043a\u0430\u043a <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t,t)\" alt=\"u^*(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg\" width=\"63\" height=\"19\" data-width=\"7.924\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.924ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0438 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u043e\u0439, \u0438\u043c\u0435\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} u^*(\\hat{x}_t,t)-u^\\phi(\\hat{x}_t,t) &amp;= u^*(\\hat{x}_t,t) - \\mathbb{E}_{x_0,z} \\left[ \\hat{x}_1-x_0 \\mid \\hat{x}_t,t \\right] \\\\ &amp;= \\mathbb{E}_{x_0,z} \\left[ u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\mid \\hat{x}_t,t \\right]. \\end{aligned}\" alt=\"\\begin{aligned} u^*(\\hat{x}_t,t)-u^\\phi(\\hat{x}_t,t) &amp;= u^*(\\hat{x}_t,t) - \\mathbb{E}_{x_0,z} \\left[ \\hat{x}_1-x_0 \\mid \\hat{x}_t,t \\right] \\\\ &amp;= \\mathbb{E}_{x_0,z} \\left[ u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\mid \\hat{x}_t,t \\right]. \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/81\/81d\/81def8b7076165449c542f09e7b134cb.svg\" width=\"438\" height=\"50\" data-width=\"54.724\" data-height=\"6.227\" data-vertical-align=\"-2.548\" style=\"width: 54.724ex; height: 6.227ex; vertical-align: -2.548ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/81\/81d\/81def8b7076165449c542f09e7b134cb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/81\/81d\/81def8b7076165449c542f09e7b134cb.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041e\u0431\u043e\u0437\u043d\u0430\u0447\u0438\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\zeta = u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0).\" alt=\"\\zeta = u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a45\/a45e908b0b91a2b64e1f3352540be8a3.svg\" width=\"196\" height=\"19\" data-width=\"24.491\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 24.491ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a45\/a45e908b0b91a2b64e1f3352540be8a3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a45\/a45e908b0b91a2b64e1f3352540be8a3.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e\u0433\u0434\u0430 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c \u0441\u0440\u0435\u0434\u043d\u0438\u0445 \u043f\u043e\u043b\u0435\u0439 \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u043a\u0430\u043a:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^*(\\hat{x}_t,t)-u^\\phi(\\hat{x}_t,t) = \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right].\" alt=\"u^*(\\hat{x}_t,t)-u^\\phi(\\hat{x}_t,t) = \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7d\/7d4\/7d4c37854afbe51472e91124895fd019.svg\" width=\"288\" height=\"23\" data-width=\"36.01\" data-height=\"2.835\" data-vertical-align=\"-0.852\" style=\"width: 36.01ex; height: 2.835ex; vertical-align: -0.852ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7d\/7d4\/7d4c37854afbe51472e91124895fd019.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7d\/7d4\/7d4c37854afbe51472e91124895fd019.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u043d\u0430\u0447\u0438\u0442, \u0432\u043d\u0443\u0442\u0440\u0438 \u0438\u0434\u0435\u0430\u043b\u044c\u043d\u043e\u0439 \u0446\u0435\u043b\u0438 \u0441\u0442\u043e\u0438\u0442 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432\u0438\u0434\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\left\\| \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right] \\right\\|_2^2.\" alt=\"\\left\\| \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right] \\right\\|_2^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/48\/48d\/48d2c2d896b356cb620d79e84e648eac.svg\" width=\"142\" height=\"26\" data-width=\"17.729\" data-height=\"3.241\" data-vertical-align=\"-1.055\" style=\"width: 17.729ex; height: 3.241ex; vertical-align: -1.055ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/48\/48d\/48d2c2d896b356cb620d79e84e648eac.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/48\/48d\/48d2c2d896b356cb620d79e84e648eac.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u043e (\u043f\u0440\u0438\u0451\u043c \u043b\u0438\u043d\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u0438):<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\|a\\|_2^2 = \\max_s \\left[ -\\|s\\|_2^2 + 2\\langle s,a\\rangle \\right].\" alt=\"\\|a\\|_2^2 = \\max_s \\left[ -\\|s\\|_2^2 + 2\\langle s,a\\rangle \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c7\/c76\/c7627bab7df9e154afc47a11c08fe600.svg\" width=\"236\" height=\"29\" data-width=\"29.56\" data-height=\"3.624\" data-vertical-align=\"-1.247\" style=\"width: 29.56ex; height: 3.624ex; vertical-align: -1.247ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c7\/c76\/c7627bab7df9e154afc47a11c08fe600.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c7\/c76\/c7627bab7df9e154afc47a11c08fe600.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442\u0441\u044f \u043f\u0440\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"s=a\" alt=\"s=a\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/62\/623\/623cac45180e2e18919afa9196b97d82.svg\" width=\"42\" height=\"12\" data-width=\"5.275\" data-height=\"1.505\" data-vertical-align=\"-0.186\" style=\"width: 5.275ex; height: 1.505ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/62\/623\/623cac45180e2e18919afa9196b97d82.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/62\/623\/623cac45180e2e18919afa9196b97d82.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0438 \u0441\u043b\u0435\u0432\u0430, \u0438 \u0441\u043f\u0440\u0430\u0432\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"a\" alt=\"a\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg\" width=\"12\" height=\"12\" data-width=\"1.197\" data-height=\"1.02\" data-vertical-align=\"-0.023\" style=\"width: 1.197ex; height: 1.02ex; vertical-align: -0.023ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0440\u0430\u0432\u043d\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"2a\" alt=\"2a\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e36\/e36314e624d2b2ca257e1f1ecb381f93.svg\" width=\"19\" height=\"12\" data-width=\"2.328\" data-height=\"1.529\" data-vertical-align=\"-0.023\" style=\"width: 2.328ex; height: 1.529ex; vertical-align: -0.023ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e36\/e36314e624d2b2ca257e1f1ecb381f93.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e36\/e36314e624d2b2ca257e1f1ecb381f93.svg 781w\" loading=\"lazy\" decode=\"async\"\/> (<img decoding=\"async\" class=\"formula inline\" source=\"2s = 2a\" alt=\"2s = 2a\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e91\/e9163f2710aa0d5f82ed5f4e8e0c32ea.svg\" width=\"60\" height=\"14\" data-width=\"7.537\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 7.537ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e91\/e9163f2710aa0d5f82ed5f4e8e0c32ea.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e91\/e9163f2710aa0d5f82ed5f4e8e0c32ea.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043b\u044f \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0441\u043f\u0440\u0430\u0432\u0430). \u0420\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"a\" alt=\"a\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg\" width=\"12\" height=\"12\" data-width=\"1.197\" data-height=\"1.02\" data-vertical-align=\"-0.023\" style=\"width: 1.197ex; height: 1.02ex; vertical-align: -0.023ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0442, \u0447\u0442\u043e \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0442\u044c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0441\u043f\u0440\u0430\u0432\u0430 \u0432\u043c\u0435\u0441\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0432\u0430 \u043f\u0440\u0438 \u043f\u043e\u0434\u0441\u0447\u0435\u0442\u0435 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043e\u0432.<\/p>\n<p>\u041f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u044d\u0442\u043e \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u043e \u043a:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"a = \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right].\" alt=\"a = \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c6c\/c6c662c63f2b2b9631de002a743f4a46.svg\" width=\"148\" height=\"22\" data-width=\"18.439\" data-height=\"2.713\" data-vertical-align=\"-0.791\" style=\"width: 18.439ex; height: 2.713ex; vertical-align: -0.791ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c6c\/c6c662c63f2b2b9631de002a743f4a46.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c6c\/c6c662c63f2b2b9631de002a743f4a46.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e\u0433\u0434\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\left\\| \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right] \\right\\|_2^2 = \\max_s \\left[ -\\|s(\\hat{x}_t,t)\\|_2^2 + 2 \\left\\langle s(\\hat{x}_t,t), \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right] \\right\\rangle \\right].\" alt=\"\\left\\| \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right] \\right\\|_2^2 = \\max_s \\left[ -\\|s(\\hat{x}_t,t)\\|_2^2 + 2 \\left\\langle s(\\hat{x}_t,t), \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right] \\right\\rangle \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30d\/30d28457a5b8e6ff52b40d20e65a61f0.svg\" width=\"533\" height=\"32\" data-width=\"66.65\" data-height=\"3.994\" data-vertical-align=\"-1.432\" style=\"width: 66.65ex; height: 3.994ex; vertical-align: -1.432ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30d\/30d28457a5b8e6ff52b40d20e65a61f0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/30\/30d\/30d28457a5b8e6ff52b40d20e65a61f0.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a \u043a\u0430\u043a <img decoding=\"async\" class=\"formula inline\" source=\"s(\\hat{x}_t,t)\" alt=\"s(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/46\/461\/4615d0563ff7d3b23246f6e79ccdde57.svg\" width=\"54\" height=\"19\" data-width=\"6.703\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 6.703ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/46\/461\/4615d0563ff7d3b23246f6e79ccdde57.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/46\/461\/4615d0563ff7d3b23246f6e79ccdde57.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0435\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0432\u043d\u0435\u0441\u0442\u0438 \u0432\u043d\u0443\u0442\u0440\u044c \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0433\u043e \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u044f:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} &amp; -\\|s(\\hat{x}_t,t)\\|_2^2 + 2 \\left\\langle s(\\hat{x}_t,t), \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right] \\right\\rangle \\\\ &amp;= \\mathbb{E}_{x_0,z} \\left[ -\\|s(\\hat{x}_t,t)\\|_2^2 + 2 \\left\\langle s(\\hat{x}_t,t), \\zeta \\right\\rangle \\mid \\hat{x}_t,t \\right]. \\end{aligned}\" alt=\"\\begin{aligned} &amp; -\\|s(\\hat{x}_t,t)\\|_2^2 + 2 \\left\\langle s(\\hat{x}_t,t), \\mathbb{E}_{x_0,z} \\left[ \\zeta \\mid \\hat{x}_t,t \\right] \\right\\rangle \\\\ &amp;= \\mathbb{E}_{x_0,z} \\left[ -\\|s(\\hat{x}_t,t)\\|_2^2 + 2 \\left\\langle s(\\hat{x}_t,t), \\zeta \\right\\rangle \\mid \\hat{x}_t,t \\right]. \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/582\/582f600efd66d5efe0d1289ff3a8abce.svg\" width=\"345\" height=\"50\" data-width=\"43.076\" data-height=\"6.262\" data-vertical-align=\"-2.565\" style=\"width: 43.076ex; height: 6.262ex; vertical-align: -2.565ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/582\/582f600efd66d5efe0d1289ff3a8abce.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/582\/582f600efd66d5efe0d1289ff3a8abce.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0432 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0438 \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0435\u0442 \u043d\u043e\u0440\u043c\u044b \u043e\u0442 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u044f. \u041c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043b\u0438 \u0435\u0451 \u043d\u0430 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u043f\u043e \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"s\" alt=\"s\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03c\/03c7c0ace395d80182db07ae2c30f034.svg\" width=\"12\" height=\"12\" data-width=\"1.061\" data-height=\"1.023\" data-vertical-align=\"-0.023\" style=\"width: 1.061ex; height: 1.023ex; vertical-align: -0.023ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03c\/03c7c0ace395d80182db07ae2c30f034.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/03\/03c\/03c7c0ace395d80182db07ae2c30f034.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u0432\u043d\u0443\u0442\u0440\u0438 \u043e\u0436\u0438\u0434\u0430\u043d\u0438\u044f \u043e\u0441\u0442\u0430\u043b\u043e\u0441\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\zeta\" alt=\"\\zeta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3c\/3c2\/3c22ba7aade15ea2b2852cd51bb4d6d4.svg\" width=\"12\" height=\"18\" data-width=\"1.066\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.066ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3c\/3c2\/3c22ba7aade15ea2b2852cd51bb4d6d4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3c\/3c2\/3c22ba7aade15ea2b2852cd51bb4d6d4.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0418\u043c\u0435\u043d\u043d\u043e \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u044d\u0442\u043e\u0442 \u0448\u0430\u0433 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u043f\u0440\u0438\u0451\u043c\u043e\u043c \u043b\u0438\u043d\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u0438<\/strong>.<\/p>\n<p>\u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0437\u0443\u0435\u043c \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0447\u0435\u0440\u0435\u0437 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"s_\\psi(x,t) = u^*(x,t)-u_\\psi(x,t).\" alt=\"s_\\psi(x,t) = u^*(x,t)-u_\\psi(x,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d5\/d58\/d589d0803b14abff2ddeabd714df2c6e.svg\" width=\"225\" height=\"19\" data-width=\"28.138\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 28.138ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d5\/d58\/d589d0803b14abff2ddeabd714df2c6e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d5\/d58\/d589d0803b14abff2ddeabd714df2c6e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e\u0433\u0434\u0430 \u0432 \u043e\u043f\u0442\u0438\u043c\u0443\u043c\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"s_\\psi\" alt=\"s_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e34\/e34955e07c3dd64d3cbee571de339d79.svg\" width=\"18\" height=\"19\" data-width=\"2.29\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.29ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e34\/e34955e07c3dd64d3cbee571de339d79.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e34\/e34955e07c3dd64d3cbee571de339d79.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e\u043b\u0436\u0435\u043d \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0442\u044c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u^*(x,t)-u^\\phi(x,t),\" alt=\"u^*(x,t)-u^\\phi(x,t),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0ab\/0abccf8bb4a67626010a2cb0058ace94.svg\" width=\"143\" height=\"21\" data-width=\"17.866\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 17.866ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0ab\/0abccf8bb4a67626010a2cb0058ace94.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0ab\/0abccf8bb4a67626010a2cb0058ace94.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u043d\u0430\u0447\u0438\u0442, <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e\u043b\u0436\u0435\u043d \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0442\u044c \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"u^\\phi\" alt=\"u^\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/06\/068\/068b42ae9de0931089634fecf0864084.svg\" width=\"19\" height=\"21\" data-width=\"2.435\" data-height=\"2.61\" data-vertical-align=\"-0.74\" style=\"width: 2.435ex; height: 2.61ex; vertical-align: -0.74ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/06\/068\/068b42ae9de0931089634fecf0864084.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/06\/068\/068b42ae9de0931089634fecf0864084.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u041f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"s_\\psi(\\hat{x}_t,t) = u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t)\" alt=\"s_\\psi(\\hat{x}_t,t) = u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b7f\/b7f2fab2d51356285a3dcb8a9051f44a.svg\" width=\"238\" height=\"20\" data-width=\"29.805\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 29.805ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b7f\/b7f2fab2d51356285a3dcb8a9051f44a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b7f\/b7f2fab2d51356285a3dcb8a9051f44a.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\zeta = u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0)\" alt=\"\\zeta = u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/89\/897\/897ca90891d2ae04b9d33267ca2c6d75.svg\" width=\"191\" height=\"19\" data-width=\"23.862\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 23.862ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/89\/897\/897ca90891d2ae04b9d33267ca2c6d75.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/89\/897\/897ca90891d2ae04b9d33267ca2c6d75.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412 \u043c\u0430\u043a\u0441\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u043c\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435. \u041f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} &amp; -\\left\\| u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t) \\right\\|_2^2 \\\\ &amp;\\quad + 2 \\left\\langle u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t), u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\rangle. \\end{aligned}\" alt=\"\\begin{aligned} &amp; -\\left\\| u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t) \\right\\|_2^2 \\\\ &amp;\\quad + 2 \\left\\langle u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t), u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\rangle. \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e5\/e58\/e5839723c00f818a117bd1cf5b18d357.svg\" width=\"383\" height=\"52\" data-width=\"47.937\" data-height=\"6.456\" data-vertical-align=\"-2.662\" style=\"width: 47.937ex; height: 6.456ex; vertical-align: -2.662ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e5\/e58\/e5839723c00f818a117bd1cf5b18d357.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e5\/e58\/e5839723c00f818a117bd1cf5b18d357.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u042d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u043d\u043e \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u043e\u0439. \u0414\u043b\u044f \u043a\u0440\u0430\u0442\u043a\u043e\u0441\u0442\u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0438\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"a = u^*(\\hat{x}_t,t), \\qquad b = u_\\psi(\\hat{x}_t,t), \\qquad v = \\hat{x}_1-x_0.\" alt=\"a = u^*(\\hat{x}_t,t), \\qquad b = u_\\psi(\\hat{x}_t,t), \\qquad v = \\hat{x}_1-x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/81\/81a\/81a3fa0ff5422285ce5826ca8ea0362e.svg\" width=\"379\" height=\"20\" data-width=\"47.426\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 47.426ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/81\/81a\/81a3fa0ff5422285ce5826ca8ea0362e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/81\/81a\/81a3fa0ff5422285ce5826ca8ea0362e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u043e\u0433\u0434\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"-\\|a-b\\|_2^2 + 2\\langle a-b,a-v\\rangle = \\|a-v\\|_2^2 - \\|b-v\\|_2^2.\" alt=\"-\\|a-b\\|_2^2 + 2\\langle a-b,a-v\\rangle = \\|a-v\\|_2^2 - \\|b-v\\|_2^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c4b\/c4bbf7a78737dc14128ee2750b87a33c.svg\" width=\"395\" height=\"21\" data-width=\"49.405\" data-height=\"2.565\" data-vertical-align=\"-0.717\" style=\"width: 49.405ex; height: 2.565ex; vertical-align: -0.717ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c4b\/c4bbf7a78737dc14128ee2750b87a33c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c4\/c4b\/c4bbf7a78737dc14128ee2750b87a33c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u043c\u0441\u044f \u043a \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u043c \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\begin{aligned} &amp; -\\left\\| u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t) \\right\\|_2^2 \\\\ &amp;\\quad + 2 \\left\\langle u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t), u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\rangle \\\\ &amp;= \\left\\| u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2. \\end{aligned}\" alt=\"\\begin{aligned} &amp; -\\left\\| u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t) \\right\\|_2^2 \\\\ &amp;\\quad + 2 \\left\\langle u^*(\\hat{x}_t,t)-u_\\psi(\\hat{x}_t,t), u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\rangle \\\\ &amp;= \\left\\| u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2. \\end{aligned}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/145\/145acac6506a8b684d08af6153382cab.svg\" width=\"426\" height=\"82\" data-width=\"53.219\" data-height=\"10.196\" data-vertical-align=\"-4.532\" style=\"width: 53.219ex; height: 10.196ex; vertical-align: -4.532ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/145\/145acac6506a8b684d08af6153382cab.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/145\/145acac6506a8b684d08af6153382cab.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412 \u0438\u0442\u043e\u0433\u0435 \u0432\u043c\u0435\u0441\u0442\u043e:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\min_{G_\\phi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right],\" alt=\"\\min_{G_\\phi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - u^\\phi(\\hat{x}_t,t) \\right\\|_2^2 \\right],\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg\" width=\"398\" height=\"38\" data-width=\"49.693\" data-height=\"4.804\" data-vertical-align=\"-1.837\" style=\"width: 49.693ex; height: 4.804ex; vertical-align: -1.837ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7a\/7ab\/7ab0ea45b4c691a8762cc5f7e4ba53d7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u0443\u044e \u0437\u0430\u0434\u0430\u0447\u0443:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\min_{G_\\phi}\\max_{u_\\psi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 \\right].\" alt=\"\\min_{G_\\phi}\\max_{u_\\psi} \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t)-(\\hat{x}_1-x_0) \\right\\|_2^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/10\/106\/1069e6626179d2cb2d92a5e0829caba4.svg\" width=\"653\" height=\"38\" data-width=\"81.583\" data-height=\"4.804\" data-vertical-align=\"-1.837\" style=\"width: 81.583ex; height: 4.804ex; vertical-align: -1.837ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/10\/106\/1069e6626179d2cb2d92a5e0829caba4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/10\/106\/1069e6626179d2cb2d92a5e0829caba4.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u042d\u0442\u043e \u0438 \u0435\u0441\u0442\u044c \u0443\u0434\u043e\u0431\u043d\u044b\u0439 \u043b\u043e\u0441\u0441 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438. \u041e\u043d \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u0435\u043d \u0441\u043e\u0433\u043b\u0430\u0441\u043e\u0432\u0430\u043d\u0438\u044e \u0441\u0440\u0435\u0434\u043d\u0438\u0445 \u043f\u043e\u043b\u0435\u0439, \u043d\u043e \u043f\u0440\u0438 \u044d\u0442\u043e\u043c \u0437\u0430\u043f\u0438\u0441\u0430\u043d \u0447\u0435\u0440\u0435\u0437 \u043e\u0431\u044b\u0447\u043d\u044b\u0435 MSE-\u043e\u0448\u0438\u0431\u043a\u0438 \u043a \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1-x_0.\" alt=\"\\hat{x}_1-x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2b\/2b3\/2b3e9b1183963bb9065212c8a08cfe32.svg\" width=\"64\" height=\"19\" data-width=\"7.958\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.958ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2b\/2b3\/2b3e9b1183963bb9065212c8a08cfe32.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/2b\/2b3\/2b3e9b1183963bb9065212c8a08cfe32.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0420\u043e\u043b\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f: \u043e\u043d \u0432\u044b\u0443\u0447\u0438\u0432\u0430\u0435\u0442 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0442\u0435\u043a\u0443\u0449\u0435\u0433\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430. \u041f\u043e\u0441\u043b\u0435 \u044d\u0442\u043e\u0433\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043e\u043d\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u043b\u043e\u0441\u044c \u043a \u043f\u043e\u043b\u044e \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/fff\/db0\/970\/fffdb09709f7407fd8eb31cae86fc48d.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 27. \u041b\u0438\u043d\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u2014 \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0435\u043d\u0438\u0435 \u0442\u0440\u0443\u0434\u043d\u043e\u0439 \u0446\u0435\u043b\u0438 \u0441\u043e \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u043f\u043e\u043b\u0435\u043c \u0432 \u0443\u0434\u043e\u0431\u043d\u0443\u044e \u0438\u0433\u0440\u0443 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/fff\/db0\/970\/fffdb09709f7407fd8eb31cae86fc48d.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/fff\/db0\/970\/fffdb09709f7407fd8eb31cae86fc48d.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 27. \u041b\u0438\u043d\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u2014 \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0435\u043d\u0438\u0435 \u0442\u0440\u0443\u0434\u043d\u043e\u0439 \u0446\u0435\u043b\u0438 \u0441\u043e \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u043f\u043e\u043b\u0435\u043c \u0432 \u0443\u0434\u043e\u0431\u043d\u0443\u044e \u0438\u0433\u0440\u0443 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f<\/figcaption><\/div>\n<\/figure>\n<\/div>\n<\/details>\n<h3>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f<\/h3>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0441\u043e\u0431\u0435\u0440\u0451\u043c \u0432\u0441\u0451 \u0432 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f.<\/p>\n<p>\u0423 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0442\u0440\u0438 \u043c\u043e\u0434\u0435\u043b\u0438:<\/p>\n<ol>\n<li>\n<p>\u041f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*(x,t)\" alt=\"u^*(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg\" width=\"57\" height=\"18\" data-width=\"7.159\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 7.159ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3a1\/3a1a807f03f6cee6bef433886737832f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043e\u0431\u044b\u0447\u043d\u044b\u043c Flow Matching\u2019\u043e\u043c;<\/p>\n<\/li>\n<li>\n<p>\u041e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi(z)\" alt=\"G_\\phi(z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg\" width=\"46\" height=\"19\" data-width=\"5.732\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 5.732ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u0431\u0443\u0447\u0438\u0442\u044c;<\/p>\n<\/li>\n<li>\n<p>\u0412\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(x,t)\" alt=\"u_\\psi(x,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg\" width=\"59\" height=\"19\" data-width=\"7.4\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 7.4ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/afd\/afda5d27a52a9424df826cb5391c7c60.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0442\u0435\u043a\u0443\u0449\u0435\u0433\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430.<\/p>\n<\/li>\n<\/ol>\n<h4>\u0428\u0430\u0433 1: \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <\/h4>\n<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0413\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0442\u0435\u043a\u0443\u0449\u0438\u0445 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432, \u043d\u043e \u0441\u0430\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043d\u0430 \u044d\u0442\u043e\u043c \u0448\u0430\u0433\u0435 \u043d\u0435 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u0442\u0441\u044f.<\/p>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m), \\qquad t \\sim \\mathcal{U}[0,1].\" alt=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m), \\qquad t \\sim \\mathcal{U}[0,1].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg\" width=\"382\" height=\"19\" data-width=\"47.801\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 47.801ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u0430\u0442\u0435\u043c \u0441\u0442\u0440\u043e\u0438\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = \\operatorname{stopgrad}(G_\\phi(z)), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1.\" alt=\"\\hat{x}_1 = \\operatorname{stopgrad}(G_\\phi(z)), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/684\/684c01355d5fde0ee71b7ba0d01fd1a5.svg\" width=\"378\" height=\"20\" data-width=\"47.215\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 47.215ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/684\/684c01355d5fde0ee71b7ba0d01fd1a5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/684\/684c01355d5fde0ee71b7ba0d01fd1a5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0421\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"v = \\hat{x}_1 - x_0.\" alt=\"v = \\hat{x}_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg\" width=\"97\" height=\"19\" data-width=\"12.073\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 12.073ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043e\u0431\u0443\u0447\u0430\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0442\u044c \u044d\u0442\u0443 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathcal{L}_\\psi = \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t) - v \\right\\|_2^2 \\right].\" alt=\"\\mathcal{L}_\\psi = \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t) - v \\right\\|_2^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e28833dcc7ae22ca1bcff48fec9a5.svg\" width=\"357\" height=\"33\" data-width=\"44.613\" data-height=\"4.07\" data-vertical-align=\"-1.469\" style=\"width: 44.613ex; height: 4.07ex; vertical-align: -1.469ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e28833dcc7ae22ca1bcff48fec9a5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e28833dcc7ae22ca1bcff48fec9a5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u042d\u0442\u043e MSE-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0445\u043e\u0440\u043e\u0448\u0435\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438 \u0444\u0435\u0439\u043a-\u043c\u043e\u0434\u0435\u043b\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u_\\psi(x,t) \\approx u^\\phi(x,t).\" alt=\"u_\\psi(x,t) \\approx u^\\phi(x,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg\" width=\"147\" height=\"22\" data-width=\"18.359\" data-height=\"2.712\" data-vertical-align=\"-0.79\" style=\"width: 18.359ex; height: 2.712ex; vertical-align: -0.79ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0414\u0435\u043b\u0430\u0435\u043c \u0442\u0430\u043a\u0438\u0435 \u0448\u0430\u0433\u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u044f \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0437.<\/p>\n<h4>\u0428\u0430\u0433 2: \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <\/h4>\n<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u043e\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u043a\u0430\u043a \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m), \\qquad t \\sim \\mathcal{U}[0,1].\" alt=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m), \\qquad t \\sim \\mathcal{U}[0,1].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg\" width=\"382\" height=\"19\" data-width=\"47.801\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 47.801ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0432\u044b\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0431\u0435\u0437 stop-gradient:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1, \\qquad v = \\hat{x}_1 - x_0.\" alt=\"\\hat{x}_1 = G_\\phi(z), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1, \\qquad v = \\hat{x}_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/53e\/53ed3b0b89f91238496f1d4f04c65a6d.svg\" width=\"431\" height=\"20\" data-width=\"53.862\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 53.862ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/53e\/53ed3b0b89f91238496f1d4f04c65a6d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/53e\/53ed3b0b89f91238496f1d4f04c65a6d.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 \u044d\u0442\u043e\u0433\u043e \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u043c \u043b\u043e\u0441\u0441 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathcal{L}_G = \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - v \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t) - v \\right\\|_2^2 \\right].\" alt=\"\\mathcal{L}_G = \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - v \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t) - v \\right\\|_2^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b6\/b6c\/b6c97fa180a6a55f0e17960bd9d5a143.svg\" width=\"503\" height=\"33\" data-width=\"62.886\" data-height=\"4.07\" data-vertical-align=\"-1.469\" style=\"width: 62.886ex; height: 4.07ex; vertical-align: -1.469ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b6\/b6c\/b6c97fa180a6a55f0e17960bd9d5a143.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b6\/b6c\/b6c97fa180a6a55f0e17960bd9d5a143.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e \u044d\u0442\u043e\u0442 \u0448\u0430\u0433 \u043c\u0435\u043d\u044f\u0435\u0442 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0435\u0433\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0441\u0442\u0430\u043b\u043e \u0431\u043b\u0438\u0436\u0435 \u043a \u043f\u043e\u043b\u044e \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u043f\u0441\u0435\u0432\u0434\u043e\u043a\u043e\u0434 (\u0432 \u0431\u0430\u0442\u0447\u0435\u0432\u043e\u0439 \u0444\u043e\u0440\u043c\u0435), \u0447\u0442\u043e\u0431\u044b \u0435\u0449\u0451 \u043b\u0443\u0447\u0448\u0435 \u0437\u0430\u043a\u0440\u0435\u043f\u0438\u0442\u044c \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b \ud83d\ude0e<\/p>\n<ul>\n<li>\n<p>\u2699\ufe0f <strong>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c:<\/strong> \u0414\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f Flow Matching\u2019\u0430 \u0432 \u043e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440<\/p>\n<\/li>\n<li>\n<p><strong>\u0412\u0445\u043e\u0434:<\/strong> \u041f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u044b \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"\\phi\" alt=\"\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg\" width=\"12\" height=\"18\" data-width=\"1.348\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.348ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\psi\" alt=\"\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg\" width=\"12\" height=\"18\" data-width=\"1.473\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.473ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"N\" alt=\"N\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg\" width=\"16\" height=\"12\" data-width=\"2.009\" data-height=\"1.545\" style=\"width: 2.009ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0448\u0430\u0433\u043e\u0432 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0430 \u043e\u0434\u0438\u043d \u0448\u0430\u0433 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"K_\\psi\" alt=\"K_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg\" width=\"25\" height=\"19\" data-width=\"3.15\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 3.15ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0440\u0430\u0437\u043c\u0435\u0440 \u0431\u0430\u0442\u0447\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"B\" alt=\"B\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg\" width=\"14\" height=\"12\" data-width=\"1.717\" data-height=\"1.545\" style=\"width: 1.717ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><strong>\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/strong> \u041e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><strong>\u0414\u043b\u044f<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"i = 1\" alt=\"i = 1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg\" width=\"39\" height=\"14\" data-width=\"4.929\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.929ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e <img decoding=\"async\" class=\"formula inline\" source=\"N\" alt=\"N\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg\" width=\"16\" height=\"12\" data-width=\"2.009\" data-height=\"1.545\" style=\"width: 2.009ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 781w\" loading=\"lazy\" decode=\"async\"\/> <\/p>\n<ul>\n<li>\n<p><strong>\u0428\u0430\u0433 1: \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041d\u0430 \u044d\u0442\u043e\u043c \u0448\u0430\u0433\u0435 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0442\u043e\u043b\u044c\u043a\u043e <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><strong>\u0414\u043b\u044f<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"k = 1\" alt=\"k = 1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c6\/5c6f937eacd3732196734c56ec527fa4.svg\" width=\"43\" height=\"14\" data-width=\"5.327\" data-height=\"1.756\" data-vertical-align=\"-0.186\" style=\"width: 5.327ex; height: 1.756ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c6\/5c6f937eacd3732196734c56ec527fa4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c6\/5c6f937eacd3732196734c56ec527fa4.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e <img decoding=\"async\" class=\"formula inline\" source=\"K_\\psi\" alt=\"K_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg\" width=\"25\" height=\"19\" data-width=\"3.15\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 3.15ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg 781w\" loading=\"lazy\" decode=\"async\"\/> <\/p>\n<ul>\n<li>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u0431\u0430\u0442\u0447: <img decoding=\"async\" class=\"formula inline\" source=\"x_0^{(b)} \\sim \\mathcal{N}(0,I_d), \\qquad z^{(b)} \\sim \\mathcal{N}(0,I_m), \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" alt=\"x_0^{(b)} \\sim \\mathcal{N}(0,I_d), \\qquad z^{(b)} \\sim \\mathcal{N}(0,I_m), \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg\" width=\"560\" height=\"25\" data-width=\"69.948\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 69.948ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0432\u044b\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0441\u043e stop-gradient: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1^{(b)} \\gets \\operatorname{stopgrad}(G_\\phi(z^{(b)})).\" alt=\"\\hat{x}_1^{(b)} \\gets \\operatorname{stopgrad}(G_\\phi(z^{(b)})).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f8\/9f894b21a1fec7405aaf0b4fc5d93199.svg\" width=\"206\" height=\"25\" data-width=\"25.74\" data-height=\"3.072\" data-vertical-align=\"-0.971\" style=\"width: 25.74ex; height: 3.072ex; vertical-align: -0.971ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f8\/9f894b21a1fec7405aaf0b4fc5d93199.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f8\/9f894b21a1fec7405aaf0b4fc5d93199.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}\\hat{x}_1^{(b)}.\" alt=\"\\hat{x}_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}\\hat{x}_1^{(b)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg\" width=\"229\" height=\"25\" data-width=\"28.681\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 28.681ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0426\u0435\u043b\u0435\u0432\u044b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"v^{(b)} \\gets \\hat{x}_1^{(b)} - x_0^{(b)}.\" alt=\"v^{(b)} \\gets \\hat{x}_1^{(b)} - x_0^{(b)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg\" width=\"136\" height=\"25\" data-width=\"16.956\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 16.956ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043b\u043e\u0441\u0441 \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e \u0431\u0430\u0442\u0447\u0443: <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}_\\psi \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\left\\| u_\\psi(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2.\" alt=\"\\mathcal{L}_\\psi \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\left\\| u_\\psi(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/05e\/05e84a278bc4d4c1d7e56a774579e685.svg\" width=\"278\" height=\"54\" data-width=\"34.796\" data-height=\"6.784\" data-vertical-align=\"-2.827\" style=\"width: 34.796ex; height: 6.784ex; vertical-align: -2.827ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/05e\/05e84a278bc4d4c1d7e56a774579e685.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/05e\/05e84a278bc4d4c1d7e56a774579e685.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"\\psi\" alt=\"\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg\" width=\"12\" height=\"18\" data-width=\"1.473\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.473ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0448\u0430\u0433\u043e\u043c \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u0430 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}_\\psi\" alt=\"\\mathcal{L}_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fda\/fda471b66dc57d86b57e7e7c213a1c26.svg\" width=\"22\" height=\"19\" data-width=\"2.79\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.79ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fda\/fda471b66dc57d86b57e7e7c213a1c26.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fda\/fda471b66dc57d86b57e7e7c213a1c26.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u0428\u0430\u0433 2: \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041d\u0430 \u044d\u0442\u043e\u043c \u0448\u0430\u0433\u0435 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0442\u043e\u043b\u044c\u043a\u043e <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u041f\u043e\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u043a\u0430\u043a \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <strong>\u0412\u0430\u0436\u043d\u043e:<\/strong> \u043d\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c <code>torch.no_grad()<\/code> \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t^{(b)},t^{(b)})\" alt=\"u^*(\\hat{x}_t^{(b)},t^{(b)})\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fb7\/fb72f4bf3b8b98e212452d879f4db042.svg\" width=\"91\" height=\"24\" data-width=\"11.396\" data-height=\"3.026\" data-vertical-align=\"-0.947\" style=\"width: 11.396ex; height: 3.026ex; vertical-align: -0.947ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fb7\/fb72f4bf3b8b98e212452d879f4db042.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fb7\/fb72f4bf3b8b98e212452d879f4db042.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(\\hat{x}_t^{(b)},t^{(b)})\" alt=\"u_\\psi(\\hat{x}_t^{(b)},t^{(b)})\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6e\/6e0\/6e02b5a15a317dbf580a91c2f94602f2.svg\" width=\"93\" height=\"25\" data-width=\"11.638\" data-height=\"3.067\" data-vertical-align=\"-0.968\" style=\"width: 11.638ex; height: 3.067ex; vertical-align: -0.968ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6e\/6e0\/6e02b5a15a317dbf580a91c2f94602f2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6e\/6e0\/6e02b5a15a317dbf580a91c2f94602f2.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043b\u0438 <code>.detach()<\/code>\u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t^{(b)}\" alt=\"\\hat{x}_t^{(b)}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/64\/64f\/64f11a099ca8e3674708c18609c4f7bf.svg\" width=\"27\" height=\"24\" data-width=\"3.413\" data-height=\"3.026\" data-vertical-align=\"-0.947\" style=\"width: 3.413ex; height: 3.026ex; vertical-align: -0.947ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/64\/64f\/64f11a099ca8e3674708c18609c4f7bf.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/64\/64f\/64f11a099ca8e3674708c18609c4f7bf.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<\/li>\n<li>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u0431\u0430\u0442\u0447: <img decoding=\"async\" class=\"formula inline\" source=\"x_0^{(b)} \\sim \\mathcal{N}(0,I_d), \\qquad z^{(b)} \\sim \\mathcal{N}(0,I_m), \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" alt=\"x_0^{(b)} \\sim \\mathcal{N}(0,I_d), \\qquad z^{(b)} \\sim \\mathcal{N}(0,I_m), \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg\" width=\"560\" height=\"25\" data-width=\"69.948\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 69.948ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0432\u044b\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0431\u0435\u0437 stop-gradient: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1^{(b)} \\gets G_\\phi(z^{(b)}).\" alt=\"\\hat{x}_1^{(b)} \\gets G_\\phi(z^{(b)}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d9\/d95\/d956782741ee5af9b64de65b1e480e87.svg\" width=\"123\" height=\"25\" data-width=\"15.412\" data-height=\"3.072\" data-vertical-align=\"-0.971\" style=\"width: 15.412ex; height: 3.072ex; vertical-align: -0.971ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d9\/d95\/d956782741ee5af9b64de65b1e480e87.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d9\/d95\/d956782741ee5af9b64de65b1e480e87.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}\\hat{x}_1^{(b)}.\" alt=\"\\hat{x}_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}\\hat{x}_1^{(b)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg\" width=\"229\" height=\"25\" data-width=\"28.681\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 28.681ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0426\u0435\u043b\u0435\u0432\u044b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u0442\u0435\u043a\u0443\u0449\u0438\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430: <img decoding=\"async\" class=\"formula inline\" source=\"v^{(b)} \\gets \\hat{x}_1^{(b)} - x_0^{(b)}.\" alt=\"v^{(b)} \\gets \\hat{x}_1^{(b)} - x_0^{(b)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg\" width=\"136\" height=\"25\" data-width=\"16.956\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 16.956ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043b\u043e\u0441\u0441 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043f\u043e \u0431\u0430\u0442\u0447\u0443: <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}_G \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\Big[ \\left\\| u^*(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2 \\Big].\" alt=\"\\mathcal{L}_G \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\Big[ \\left\\| u^*(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2 \\Big].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3ab\/3abe7b52356a4f616a55f55c08652cc3.svg\" width=\"486\" height=\"54\" data-width=\"60.795\" data-height=\"6.784\" data-vertical-align=\"-2.827\" style=\"width: 60.795ex; height: 6.784ex; vertical-align: -2.827ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3ab\/3abe7b52356a4f616a55f55c08652cc3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3ab\/3abe7b52356a4f616a55f55c08652cc3.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"\\phi\" alt=\"\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg\" width=\"12\" height=\"18\" data-width=\"1.348\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.348ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0448\u0430\u0433\u043e\u043c \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u0430 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}_G\" alt=\"\\mathcal{L}_G\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/379\/379a362d083dc9ac29c2b8faba53f955.svg\" width=\"24\" height=\"18\" data-width=\"3.006\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 3.006ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/379\/379a362d083dc9ac29c2b8faba53f955.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/379\/379a362d083dc9ac29c2b8faba53f955.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u041f\u043e\u0441\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0435 \u043d\u0443\u0436\u043d\u044b \u043d\u0438 \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043d\u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041c\u044b \u043f\u0440\u043e\u0441\u0442\u043e \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u043b\u0430\u0442\u0435\u043d\u0442\u043d\u044b\u0439 \u0448\u0443\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"z \\sim \\mathcal{N}(0,I_m)\" alt=\"z \\sim \\mathcal{N}(0,I_m)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg\" width=\"102\" height=\"19\" data-width=\"12.769\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.769ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418 \u043e\u0434\u0438\u043d \u0440\u0430\u0437 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z).\" alt=\"\\hat{x}_1 = G_\\phi(z).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg\" width=\"93\" height=\"20\" data-width=\"11.66\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 11.66ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u0430\u044f Flow Matching-\u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044f \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u0438\u043c \u0448\u0430\u0433\u043e\u043c.<\/p>\n<p>\u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0441\u043a\u0440\u044b\u0442\u044b\u0439 \u0431\u043b\u043e\u043a \u2014 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u044b\u0439 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438.<\/p>\n<details class=\"spoiler\">\n<summary>\u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435<\/summary>\n<div class=\"spoiler__content\">\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u044e\u0430\u043d\u0441\u044b \u043f\u0440\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438.<\/p>\n<p>\u041f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432\u043e \u0432\u0440\u0435\u043c\u044f \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 \u043d\u0435 \u043e\u0431\u0443\u0447\u0430\u0435\u0442\u0441\u044f. \u041e\u043d\u043e \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u0442, \u043a\u0430\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e \u043f\u0435\u0440\u0435\u043d\u043e\u0441\u0438\u0442\u044c \u0448\u0443\u043c \u0432 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0445. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043e\u0434\u0438\u043d \u0440\u0430\u0437 \u043f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c \u0435\u0433\u043e \u0432 \u0440\u0435\u0436\u0438\u043c <code>eval<\/code> \u0438 \u0437\u0430\u043c\u043e\u0440\u0430\u0436\u0438\u0432\u0430\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u0434\u043b\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\texttt{u\\_star.eval()},  \\qquad \\texttt{u\\_star.requires\\_grad\\_(False)}.\" alt=\"\\texttt{u\\_star.eval()},  \\qquad \\texttt{u\\_star.requires\\_grad\\_(False)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a0\/a09\/a097ae026b2ab3a0110685ec9d0377a8.svg\" width=\"439\" height=\"18\" data-width=\"54.859\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 54.859ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a0\/a09\/a097ae026b2ab3a0110685ec9d0377a8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a0\/a09\/a097ae026b2ab3a0110685ec9d0377a8.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041e\u0434\u043d\u0430\u043a\u043e \u0437\u0434\u0435\u0441\u044c \u0435\u0441\u0442\u044c \u0432\u0430\u0436\u043d\u0430\u044f \u0442\u043e\u043d\u043a\u043e\u0441\u0442\u044c. \u0417\u0430\u043c\u043e\u0440\u043e\u0437\u0438\u0442\u044c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u043c\u043e\u0434\u0435\u043b\u0438 \u2014 \u043d\u0435 \u0442\u043e \u0436\u0435 \u0441\u0430\u043c\u043e\u0435, \u0447\u0442\u043e \u0437\u0430\u043f\u0440\u0435\u0442\u0438\u0442\u044c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0447\u0435\u0440\u0435\u0437 \u0435\u0451 \u0432\u0445\u043e\u0434. \u041f\u0440\u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0435 \u0434\u043e\u043b\u0436\u043d\u044b \u043c\u0435\u043d\u044f\u0442\u044c\u0441\u044f, \u043d\u043e \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0434\u043e\u043b\u0436\u0435\u043d \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442\u044c \u0447\u0435\u0440\u0435\u0437 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t,t)\" alt=\"u^*(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg\" width=\"63\" height=\"19\" data-width=\"7.924\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.924ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043a \u0442\u043e\u0447\u043a\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0432\u044b\u0445\u043e\u0434\u0430 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi(z)\" alt=\"G_\\phi(z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg\" width=\"46\" height=\"19\" data-width=\"5.732\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 5.732ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043d\u0435\u043b\u044c\u0437\u044f \u0441\u0447\u0438\u0442\u0430\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t,t)\" alt=\"u^*(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg\" width=\"63\" height=\"19\" data-width=\"7.924\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.924ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432\u043d\u0443\u0442\u0440\u0438 <code>torch.no_grad()<\/code> \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c <code>.detach()<\/code>\u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/03c\/562\/630\/03c562630daf716519dc8c18b50635b1.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 28. \u0417\u0430\u043c\u043e\u0440\u043e\u0437\u043a\u0430 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 u^* \u0438 u_\\psi \u043f\u0440\u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430, \u043d\u043e \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0434\u043e\u043b\u0436\u0435\u043d \u043f\u0440\u043e\u0439\u0442\u0438 \u0447\u0435\u0440\u0435\u0437 \u0438\u0445 \u0432\u0445\u043e\u0434 \\hat{x}t \u043e\u0431\u0440\u0430\u0442\u043d\u043e \u043a G\\phi\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/03c\/562\/630\/03c562630daf716519dc8c18b50635b1.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/03c\/562\/630\/03c562630daf716519dc8c18b50635b1.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 28. \u0417\u0430\u043c\u043e\u0440\u043e\u0437\u043a\u0430 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 u^* \u0438 u_\\psi \u043f\u0440\u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430, \u043d\u043e \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0434\u043e\u043b\u0436\u0435\u043d \u043f\u0440\u043e\u0439\u0442\u0438 \u0447\u0435\u0440\u0435\u0437 \u0438\u0445 \u0432\u0445\u043e\u0434 \\hat{x}t \u043e\u0431\u0440\u0430\u0442\u043d\u043e \u043a G\\phi<\/figcaption><\/div>\n<\/figure>\n<p>\ud83d\udca1 <strong>\u0427\u0430\u0441\u0442\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430:<\/strong> \u043f\u0440\u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043d\u0435\u043b\u044c\u0437\u044f \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c <code>torch.no_grad()<\/code> \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t,t)\" alt=\"u^*(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg\" width=\"63\" height=\"19\" data-width=\"7.924\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.924ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(\\hat{x}_t,t)\" alt=\"u_\\psi(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg\" width=\"65\" height=\"20\" data-width=\"8.166\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 8.166ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043b\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c <code>.detach()<\/code>\u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u044d\u0442\u0438\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0437\u0430\u043c\u043e\u0440\u043e\u0436\u0435\u043d\u044b, \u043d\u043e \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0434\u043e\u043b\u0436\u0435\u043d \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442\u044c \u0447\u0435\u0440\u0435\u0437 \u0438\u0445 \u0432\u0445\u043e\u0434 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043a \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0412 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u043a\u043e\u0434\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u043d\u0438\u0436\u0435 \u043e\u0431\u044b\u0447\u043d\u043e \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0431\u0430\u0442\u0447\u0430\u043c\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0434\u043b\u044f \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"x_0\" alt=\"x_0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg\" width=\"18\" height=\"12\" data-width=\"2.282\" data-height=\"1.375\" data-vertical-align=\"-0.375\" style=\"width: 2.282ex; height: 1.375ex; vertical-align: -0.375ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3e\/3e0\/3e0d691f3a530e6c7e079636f20c111b.svg 780w,&#10;     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src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"v\" alt=\"v\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9e\/9e3\/9e3669d19b675bd57058fd4664205d2a.svg\" width=\"12\" height=\"12\" data-width=\"1.097\" data-height=\"1.027\" data-vertical-align=\"-0.025\" style=\"width: 1.097ex; height: 1.027ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9e\/9e3\/9e3669d19b675bd57058fd4664205d2a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9e\/9e3\/9e3669d19b675bd57058fd4664205d2a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043c\u0435\u044e\u0442 \u0444\u043e\u0440\u043c\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"[B, C, H, W]\" alt=\"[B, C, H, W]\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/28\/289\/2898c244b7172c98e234cde0aabfbc84.svg\" width=\"97\" height=\"18\" data-width=\"12.093\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 12.093ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/28\/289\/2898c244b7172c98e234cde0aabfbc84.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/28\/289\/2898c244b7172c98e234cde0aabfbc84.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u0432\u0440\u0435\u043c\u044f <img decoding=\"async\" class=\"formula inline\" source=\"t\" alt=\"t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg\" width=\"12\" height=\"12\" data-width=\"0.817\" data-height=\"1.441\" data-vertical-align=\"-0.025\" style=\"width: 0.817ex; height: 1.441ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e3\/e35\/e358efa489f58062f10dd7316b65649e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0443\u0434\u043e\u0431\u043d\u043e \u0445\u0440\u0430\u043d\u0438\u0442\u044c \u0432 \u0444\u043e\u0440\u043c\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"[B, 1, 1, 1]\" alt=\"[B, 1, 1, 1]\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/af5\/af51ba9d7e400fb8d6e52c6033cbf3fe.svg\" width=\"75\" height=\"18\" data-width=\"9.387\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 9.387ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/af5\/af51ba9d7e400fb8d6e52c6033cbf3fe.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/af\/af5\/af51ba9d7e400fb8d6e52c6033cbf3fe.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0447\u0442\u043e\u0431\u044b \u043e\u043d\u043e \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 broadcast\u2019\u0438\u043b\u043e\u0441\u044c \u043f\u043e \u043a\u0430\u043d\u0430\u043b\u0430\u043c \u0438 \u043f\u0438\u043a\u0441\u0435\u043b\u044f\u043c.<\/p>\n<p>\u0415\u0449\u0451 \u0440\u0430\u0437 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f, \u043d\u043e \u0441 \u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u044b\u043c \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435\u043c.<\/p>\n<h4>\u0428\u0430\u0433 1: \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <\/h4>\n<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0442\u044c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0413\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0442\u0435\u043a\u0443\u0449\u0438\u0445 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432, \u043d\u043e \u0441\u0430\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043d\u0430 \u044d\u0442\u043e\u043c \u0448\u0430\u0433\u0435 \u043d\u0435 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u0442\u0441\u044f.<\/p>\n<p>\u041f\u043e\u044d\u0442\u043e\u043c\u0443:<\/p>\n<ul>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c \u0432 \u0440\u0435\u0436\u0438\u043c <code>train<\/code> \u0438 \u0440\u0430\u0437\u0440\u0435\u0448\u0430\u0435\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u044b \u043f\u043e \u0435\u0433\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c;<\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c \u0432 \u0440\u0435\u0436\u0438\u043c <code>eval<\/code> \u0438 \u0437\u0430\u043c\u043e\u0440\u0430\u0436\u0438\u0432\u0430\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b;<\/p>\n<\/li>\n<li>\n<p>\u0432\u044b\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1=G_\\phi(z)\" alt=\"\\hat{x}_1=G_\\phi(z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6fd\/6fd85a3d9abb649d51e5d5cc3e05b231.svg\" width=\"88\" height=\"20\" data-width=\"11.031\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 11.031ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6fd\/6fd85a3d9abb649d51e5d5cc3e05b231.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6f\/6fd\/6fd85a3d9abb649d51e5d5cc3e05b231.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0441\u043e stop-gradient, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0447\u0435\u0440\u0435\u0437 <code>torch.no_grad()<\/code> \u0438\u043b\u0438 <code>.detach()<\/code>;<\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0430 \u044d\u0442\u043e\u043c \u0448\u0430\u0433\u0435 \u043d\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c.<\/p>\n<\/li>\n<\/ul>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m), \\qquad t \\sim \\mathcal{U}[0,1].\" alt=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m), \\qquad t \\sim \\mathcal{U}[0,1].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg\" width=\"382\" height=\"19\" data-width=\"47.801\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 47.801ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0417\u0430\u0442\u0435\u043c \u0441\u0442\u0440\u043e\u0438\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = \\operatorname{stopgrad}(G_\\phi(z)), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1.\" alt=\"\\hat{x}_1 = \\operatorname{stopgrad}(G_\\phi(z)), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/684\/684c01355d5fde0ee71b7ba0d01fd1a5.svg\" width=\"378\" height=\"20\" data-width=\"47.215\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 47.215ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/684\/684c01355d5fde0ee71b7ba0d01fd1a5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/684\/684c01355d5fde0ee71b7ba0d01fd1a5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0421\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0439 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"v = \\hat{x}_1 - x_0.\" alt=\"v = \\hat{x}_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg\" width=\"97\" height=\"19\" data-width=\"12.073\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 12.073ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9bc\/9bceec057566d5a5730c0c5b1d0ffed9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043e\u0431\u0443\u0447\u0430\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0442\u044c \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathcal{L}_\\psi = \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t) - v \\right\\|_2^2 \\right].\" alt=\"\\mathcal{L}_\\psi = \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u_\\psi(\\hat{x}_t,t) - v \\right\\|_2^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e28833dcc7ae22ca1bcff48fec9a5.svg\" width=\"357\" height=\"33\" data-width=\"44.613\" data-height=\"4.07\" data-vertical-align=\"-1.469\" style=\"width: 44.613ex; height: 4.07ex; vertical-align: -1.469ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e28833dcc7ae22ca1bcff48fec9a5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/de\/de4\/de4e28833dcc7ae22ca1bcff48fec9a5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u042d\u0442\u043e \u043e\u0431\u044b\u0447\u043d\u0430\u044f MSE-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0445\u043e\u0440\u043e\u0448\u0435\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"u_\\psi(x,t) \\approx u^\\phi(x,t).\" alt=\"u_\\psi(x,t) \\approx u^\\phi(x,t).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg\" width=\"147\" height=\"22\" data-width=\"18.359\" data-height=\"2.712\" data-vertical-align=\"-0.79\" style=\"width: 18.359ex; height: 2.712ex; vertical-align: -0.79ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be3e2b7e960580c5f1c1b81c7306f02.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<h4>\u0428\u0430\u0433 2: \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <\/h4>\n<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041f\u043e\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u043a\u0430\u043a \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p>\u041f\u043e\u044d\u0442\u043e\u043c\u0443:<\/p>\n<ul>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c \u0432 \u0440\u0435\u0436\u0438\u043c <code>train<\/code> \u0438 \u0440\u0430\u0437\u0440\u0435\u0448\u0430\u0435\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u044b \u043f\u043e \u0435\u0433\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c;<\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0432 \u0440\u0435\u0436\u0438\u043c\u0435 <code>eval<\/code> \u0441 \u0437\u0430\u043c\u043e\u0440\u043e\u0436\u0435\u043d\u043d\u044b\u043c\u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438;<\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c \u0432 \u0440\u0435\u0436\u0438\u043c <code>eval<\/code> \u0438 \u0437\u0430\u043c\u043e\u0440\u0430\u0436\u0438\u0432\u0430\u0435\u043c \u0435\u0433\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b;<\/p>\n<\/li>\n<li>\n<p>\u043d\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c <code>torch.no_grad()<\/code> \u0432\u043e\u043a\u0440\u0443\u0433 <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t,t)\" alt=\"u^*(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg\" width=\"63\" height=\"19\" data-width=\"7.924\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.924ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(\\hat{x}_t,t)\" alt=\"u_\\psi(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg\" width=\"65\" height=\"20\" data-width=\"8.166\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 8.166ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg 781w\" loading=\"lazy\" decode=\"async\"\/>;<\/p>\n<\/li>\n<li>\n<p>\u043d\u0435 \u0434\u0435\u043b\u0430\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t.\\text{detach}()\" alt=\"\\hat{x}_t.\\text{detach}()\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/dd\/ddd\/ddd6570ad4d2d7347945593136ca1d07.svg\" width=\"91\" height=\"19\" data-width=\"11.362\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 11.362ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/dd\/ddd\/ddd6570ad4d2d7347945593136ca1d07.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/dd\/ddd\/ddd6570ad4d2d7347945593136ca1d07.svg 781w\" loading=\"lazy\" decode=\"async\"\/>;<\/p>\n<\/li>\n<li>\n<p>\u043f\u0440\u043e\u0432\u043e\u0434\u0438\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0447\u0435\u0440\u0435\u0437 <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t,t)\" alt=\"u^*(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg\" width=\"63\" height=\"19\" data-width=\"7.924\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.924ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(\\hat{x}_t,t)\" alt=\"u_\\psi(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg\" width=\"65\" height=\"20\" data-width=\"8.166\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 8.166ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1\" alt=\"\\hat{x}_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg\" width=\"18\" height=\"19\" data-width=\"2.282\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.282ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fe\/fed\/fedd9b0fae9fd1b27485d15734d14c86.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0434\u0430\u043b\u0435\u0435 \u0432 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<\/li>\n<\/ul>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m), \\qquad t \\sim \\mathcal{U}[0,1].\" alt=\"x_0 \\sim \\mathcal{N}(0,I_d), \\qquad z \\sim \\mathcal{N}(0,I_m), \\qquad t \\sim \\mathcal{U}[0,1].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg\" width=\"382\" height=\"19\" data-width=\"47.801\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 47.801ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e9\/e99\/e997536560c5adb61abc9a26b7266cc9.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0432\u044b\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0431\u0435\u0437 stop-gradient:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1, \\qquad v = \\hat{x}_1 - x_0.\" alt=\"\\hat{x}_1 = G_\\phi(z), \\qquad \\hat{x}_t = (1-t)x_0 + t\\hat{x}_1, \\qquad v = \\hat{x}_1 - x_0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/53e\/53ed3b0b89f91238496f1d4f04c65a6d.svg\" width=\"431\" height=\"20\" data-width=\"53.862\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 53.862ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/53e\/53ed3b0b89f91238496f1d4f04c65a6d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/53e\/53ed3b0b89f91238496f1d4f04c65a6d.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 \u044d\u0442\u043e\u0433\u043e \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u043c \u043b\u043e\u0441\u0441 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\mathcal{L}_G = \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - v \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t) - v \\right\\|_2^2 \\right].\" alt=\"\\mathcal{L}_G = \\mathbb{E}_{t,\\,x_0\\sim\\mathcal{N}(0,I_d),\\,z\\sim\\mathcal{N}(0,I_m)} \\left[ \\left\\| u^*(\\hat{x}_t,t) - v \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t,t) - v \\right\\|_2^2 \\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b6\/b6c\/b6c97fa180a6a55f0e17960bd9d5a143.svg\" width=\"503\" height=\"33\" data-width=\"62.886\" data-height=\"4.07\" data-vertical-align=\"-1.469\" style=\"width: 62.886ex; height: 4.07ex; vertical-align: -1.469ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b6\/b6c\/b6c97fa180a6a55f0e17960bd9d5a143.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b6\/b6c\/b6c97fa180a6a55f0e17960bd9d5a143.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e \u044d\u0442\u043e\u0442 \u0448\u0430\u0433 \u043c\u0435\u043d\u044f\u0435\u0442 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043b\u0435 \u0435\u0433\u043e \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0441\u0442\u0430\u043b\u043e \u0431\u043b\u0438\u0436\u0435 \u043a \u043f\u043e\u043b\u044e \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<ul>\n<li>\n<p>\u2699\ufe0f <strong>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c:<\/strong> \u0414\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f Flow Matching\u2019\u0430 \u0432 \u043e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440<\/p>\n<\/li>\n<li>\n<p><strong>\u0412\u0445\u043e\u0434:<\/strong> \u041f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u044b \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"\\phi\" alt=\"\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg\" width=\"12\" height=\"18\" data-width=\"1.348\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.348ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\psi\" alt=\"\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg\" width=\"12\" height=\"18\" data-width=\"1.473\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.473ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"N\" alt=\"N\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg\" width=\"16\" height=\"12\" data-width=\"2.009\" data-height=\"1.545\" style=\"width: 2.009ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0448\u0430\u0433\u043e\u0432 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0430 \u043e\u0434\u0438\u043d \u0448\u0430\u0433 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"K_\\psi\" alt=\"K_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg\" width=\"25\" height=\"19\" data-width=\"3.15\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 3.15ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0440\u0430\u0437\u043c\u0435\u0440 \u0431\u0430\u0442\u0447\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"B\" alt=\"B\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg\" width=\"14\" height=\"12\" data-width=\"1.717\" data-height=\"1.545\" style=\"width: 1.717ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><strong>\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/strong> \u041e\u0434\u043d\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0440\u0435\u0436\u0438\u043c <code>eval<\/code><\/p>\n<p>\u0417\u0430\u043c\u043e\u0440\u0430\u0436\u0438\u0432\u0430\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>: <code>requires_grad_(False)<\/code><\/p>\n<\/li>\n<li>\n<p><strong>\u0414\u043b\u044f<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"i = 1\" alt=\"i = 1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg\" width=\"39\" height=\"14\" data-width=\"4.929\" data-height=\"1.692\" data-vertical-align=\"-0.186\" style=\"width: 4.929ex; height: 1.692ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/590\/5905475576a21ecdafdaab879ff45aff.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e <img decoding=\"async\" class=\"formula inline\" source=\"N\" alt=\"N\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg\" width=\"16\" height=\"12\" data-width=\"2.009\" data-height=\"1.545\" style=\"width: 2.009ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8d\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<ul>\n<li>\n<p><strong>\u0428\u0430\u0433 1: \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041d\u0430 \u044d\u0442\u043e\u043c \u0448\u0430\u0433\u0435 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0442\u043e\u043b\u044c\u043a\u043e <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u041f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0440\u0435\u0436\u0438\u043c <code>train<\/code><\/p>\n<p>\u0420\u0430\u0437\u0440\u0435\u0448\u0430\u0435\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u044b \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>: <code>requires_grad_(True)<\/code><\/p>\n<p>\u041f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0440\u0435\u0436\u0438\u043c <code>eval<\/code><\/p>\n<p>\u0417\u0430\u043c\u043e\u0440\u0430\u0436\u0438\u0432\u0430\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>: <code>requires_grad_(False)<\/code><\/p>\n<\/li>\n<li>\n<p><strong>\u0414\u043b\u044f<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"k = 1\" alt=\"k = 1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c6\/5c6f937eacd3732196734c56ec527fa4.svg\" width=\"43\" height=\"14\" data-width=\"5.327\" data-height=\"1.756\" data-vertical-align=\"-0.186\" style=\"width: 5.327ex; height: 1.756ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c6\/5c6f937eacd3732196734c56ec527fa4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c6\/5c6f937eacd3732196734c56ec527fa4.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e <img decoding=\"async\" class=\"formula inline\" source=\"K_\\psi\" alt=\"K_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg\" width=\"25\" height=\"19\" data-width=\"3.15\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 3.15ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/42\/425\/42595af87039305ac7555c04383a3abf.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<ul>\n<li>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u0431\u0430\u0442\u0447: <img decoding=\"async\" class=\"formula inline\" source=\"x_0^{(b)} \\sim \\mathcal{N}(0,I_d), \\qquad z^{(b)} \\sim \\mathcal{N}(0,I_m), \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" alt=\"x_0^{(b)} \\sim \\mathcal{N}(0,I_d), \\qquad z^{(b)} \\sim \\mathcal{N}(0,I_m), \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg\" width=\"560\" height=\"25\" data-width=\"69.948\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 69.948ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0432\u044b\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0441\u043e stop-gradient: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1^{(b)} \\gets \\operatorname{stopgrad}(G_\\phi(z^{(b)})).\" alt=\"\\hat{x}_1^{(b)} \\gets \\operatorname{stopgrad}(G_\\phi(z^{(b)})).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f8\/9f894b21a1fec7405aaf0b4fc5d93199.svg\" width=\"206\" height=\"25\" data-width=\"25.74\" data-height=\"3.072\" data-vertical-align=\"-0.971\" style=\"width: 25.74ex; height: 3.072ex; vertical-align: -0.971ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f8\/9f894b21a1fec7405aaf0b4fc5d93199.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f8\/9f894b21a1fec7405aaf0b4fc5d93199.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}\\hat{x}_1^{(b)}.\" alt=\"\\hat{x}_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}\\hat{x}_1^{(b)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg\" width=\"229\" height=\"25\" data-width=\"28.681\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 28.681ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0426\u0435\u043b\u0435\u0432\u044b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"v^{(b)} \\gets \\hat{x}_1^{(b)} - x_0^{(b)}.\" alt=\"v^{(b)} \\gets \\hat{x}_1^{(b)} - x_0^{(b)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg\" width=\"136\" height=\"25\" data-width=\"16.956\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 16.956ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043b\u043e\u0441\u0441 \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e \u0431\u0430\u0442\u0447\u0443: <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}_\\psi \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\left\\| u_\\psi(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2.\" alt=\"\\mathcal{L}_\\psi \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\left\\| u_\\psi(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/05e\/05e84a278bc4d4c1d7e56a774579e685.svg\" width=\"278\" height=\"54\" data-width=\"34.796\" data-height=\"6.784\" data-vertical-align=\"-2.827\" style=\"width: 34.796ex; height: 6.784ex; vertical-align: -2.827ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/05e\/05e84a278bc4d4c1d7e56a774579e685.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/05e\/05e84a278bc4d4c1d7e56a774579e685.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"\\psi\" alt=\"\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg\" width=\"12\" height=\"18\" data-width=\"1.473\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.473ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a11\/a11bd56a0ff5973a5604bb3fc9142b1d.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0448\u0430\u0433\u043e\u043c \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u0430 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}_\\psi\" alt=\"\\mathcal{L}_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fda\/fda471b66dc57d86b57e7e7c213a1c26.svg\" width=\"22\" height=\"19\" data-width=\"2.79\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.79ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fda\/fda471b66dc57d86b57e7e7c213a1c26.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fda\/fda471b66dc57d86b57e7e7c213a1c26.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u0428\u0430\u0433 2: \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041d\u0430 \u044d\u0442\u043e\u043c \u0448\u0430\u0433\u0435 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0442\u043e\u043b\u044c\u043a\u043e <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u041f\u043e\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u043a\u0430\u043a \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <strong>\u0412\u0430\u0436\u043d\u043e:<\/strong> \u043d\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c <code>torch.no_grad()<\/code> \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t^{(b)},t^{(b)})\" alt=\"u^*(\\hat{x}_t^{(b)},t^{(b)})\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fb7\/fb72f4bf3b8b98e212452d879f4db042.svg\" width=\"91\" height=\"24\" data-width=\"11.396\" data-height=\"3.026\" data-vertical-align=\"-0.947\" style=\"width: 11.396ex; height: 3.026ex; vertical-align: -0.947ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fb7\/fb72f4bf3b8b98e212452d879f4db042.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fb7\/fb72f4bf3b8b98e212452d879f4db042.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(\\hat{x}_t^{(b)},t^{(b)})\" alt=\"u_\\psi(\\hat{x}_t^{(b)},t^{(b)})\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6e\/6e0\/6e02b5a15a317dbf580a91c2f94602f2.svg\" width=\"93\" height=\"25\" data-width=\"11.638\" data-height=\"3.067\" data-vertical-align=\"-0.968\" style=\"width: 11.638ex; height: 3.067ex; vertical-align: -0.968ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6e\/6e0\/6e02b5a15a317dbf580a91c2f94602f2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/6e\/6e0\/6e02b5a15a317dbf580a91c2f94602f2.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0440\u0435\u0436\u0438\u043c <code>train<\/code><\/p>\n<p>\u0420\u0430\u0437\u0440\u0435\u0448\u0430\u0435\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u044b \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>: <code>requires_grad_(True)<\/code> \u041f\u0435\u0440\u0435\u0432\u043e\u0434\u0438\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0440\u0435\u0436\u0438\u043c <code>eval<\/code> \u0417\u0430\u043c\u043e\u0440\u0430\u0436\u0438\u0432\u0430\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>: <code>requires_grad_(False)<\/code> <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u0441\u0442\u0430\u0451\u0442\u0441\u044f \u0432 \u0440\u0435\u0436\u0438\u043c\u0435 <code>eval<\/code> \u0438 \u0441 \u0437\u0430\u043c\u043e\u0440\u043e\u0436\u0435\u043d\u043d\u044b\u043c\u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438<\/p>\n<\/li>\n<li>\n<p>\u0421\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u0431\u0430\u0442\u0447: <img decoding=\"async\" class=\"formula inline\" source=\"x_0^{(b)} \\sim \\mathcal{N}(0,I_d), \\qquad z^{(b)} \\sim \\mathcal{N}(0,I_m), \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" alt=\"x_0^{(b)} \\sim \\mathcal{N}(0,I_d), \\qquad z^{(b)} \\sim \\mathcal{N}(0,I_m), \\qquad t^{(b)} \\sim \\mathcal{U}[0,1], \\qquad b=1,\\ldots,B\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg\" width=\"560\" height=\"25\" data-width=\"69.948\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 69.948ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/59\/592\/592693af2078399e8d28a7edd255156f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0432\u044b\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0431\u0435\u0437 stop-gradient: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1^{(b)} \\gets G_\\phi(z^{(b)}).\" alt=\"\\hat{x}_1^{(b)} \\gets G_\\phi(z^{(b)}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d9\/d95\/d956782741ee5af9b64de65b1e480e87.svg\" width=\"123\" height=\"25\" data-width=\"15.412\" data-height=\"3.072\" data-vertical-align=\"-0.971\" style=\"width: 15.412ex; height: 3.072ex; vertical-align: -0.971ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d9\/d95\/d956782741ee5af9b64de65b1e480e87.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/d9\/d95\/d956782741ee5af9b64de65b1e480e87.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0442\u0440\u043e\u0438\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}\\hat{x}_1^{(b)}.\" alt=\"\\hat{x}_t^{(b)} \\gets (1-t^{(b)})x_0^{(b)} + t^{(b)}\\hat{x}_1^{(b)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg\" width=\"229\" height=\"25\" data-width=\"28.681\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 28.681ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c90\/c907d8ac3f2581e86ee419e07ef9f0e1.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0426\u0435\u043b\u0435\u0432\u044b\u0435 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u0442\u0435\u043a\u0443\u0449\u0438\u0445 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430: <img decoding=\"async\" class=\"formula inline\" source=\"v^{(b)} \\gets \\hat{x}_1^{(b)} - x_0^{(b)}.\" alt=\"v^{(b)} \\gets \\hat{x}_1^{(b)} - x_0^{(b)}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg\" width=\"136\" height=\"25\" data-width=\"16.956\" data-height=\"3.108\" data-vertical-align=\"-0.988\" style=\"width: 16.956ex; height: 3.108ex; vertical-align: -0.988ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0d\/b0da277a312253dc618e676758410a80.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0421\u0447\u0438\u0442\u0430\u0435\u043c \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043b\u043e\u0441\u0441 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043f\u043e \u0431\u0430\u0442\u0447\u0443: <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}_G \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\Big[ \\left\\| u^*(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2 \\Big].\" alt=\"\\mathcal{L}_G \\gets \\frac{1}{B} \\sum_{b=1}^{B} \\Big[ \\left\\| u^*(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2 - \\left\\| u_\\psi(\\hat{x}_t^{(b)},t^{(b)}) - v^{(b)} \\right\\|_2^2 \\Big].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3ab\/3abe7b52356a4f616a55f55c08652cc3.svg\" width=\"486\" height=\"54\" data-width=\"60.795\" data-height=\"6.784\" data-vertical-align=\"-2.827\" style=\"width: 60.795ex; height: 6.784ex; vertical-align: -2.827ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3ab\/3abe7b52356a4f616a55f55c08652cc3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3ab\/3abe7b52356a4f616a55f55c08652cc3.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u041e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"\\phi\" alt=\"\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg\" width=\"12\" height=\"18\" data-width=\"1.348\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.348ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1e\/1ed\/1ed346930917426bc46d41e22cc525ec.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0448\u0430\u0433\u043e\u043c \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u0430 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{L}_G\" alt=\"\\mathcal{L}_G\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/379\/379a362d083dc9ac29c2b8faba53f955.svg\" width=\"24\" height=\"18\" data-width=\"3.006\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 3.006ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/379\/379a362d083dc9ac29c2b8faba53f955.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/379\/379a362d083dc9ac29c2b8faba53f955.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u041f\u043e\u0441\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0435 \u043d\u0443\u0436\u043d\u044b \u043d\u0438 \u043f\u043e\u043b\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043d\u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u041c\u044b \u043f\u0440\u043e\u0441\u0442\u043e \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u0435\u043c \u043b\u0430\u0442\u0435\u043d\u0442\u043d\u044b\u0439 \u0448\u0443\u043c:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"z \\sim \\mathcal{N}(0,I_m)\" alt=\"z \\sim \\mathcal{N}(0,I_m)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg\" width=\"102\" height=\"19\" data-width=\"12.769\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 12.769ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/14\/14b\/14b4ab267e43748ab93c2bf94635b03c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418 \u043e\u0434\u0438\u043d \u0440\u0430\u0437 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"\\hat{x}_1 = G_\\phi(z).\" alt=\"\\hat{x}_1 = G_\\phi(z).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg\" width=\"93\" height=\"20\" data-width=\"11.66\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 11.66ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/86\/86c\/86ca352bb4a3553d267631155f2f6f6a.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0422\u0430\u043a, \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u0430\u044f Flow Matching-\u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044f \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u0438\u043c \u0448\u0430\u0433\u043e\u043c.<\/p>\n<\/div>\n<\/details>\n<p>\u0423\u0440\u0430, \u043c\u044b \u043d\u0430 \u0444\u0438\u043d\u0438\u0448\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439! \u041c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 Flow Matching \u0438 \u043a\u0430\u043a \u0435\u0433\u043e \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c. \u041e\u0441\u0442\u0430\u043b\u043e\u0441\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0431\u0441\u0443\u0434\u0438\u0442\u044c \u0434\u0435\u0442\u0430\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0438 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043d\u0430 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b! \ud83d\ude0e<\/p>\n<details class=\"spoiler\">\n<summary>\u041f\u0430\u0440\u0430 \u0434\u0435\u0442\u0430\u043b\u0435\u0439<\/summary>\n<div class=\"spoiler__content\">\n<p>\u041f\u0435\u0440\u0435\u0447\u0438\u0441\u043b\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0434\u0435\u0442\u0430\u043b\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432\u0430\u0436\u043d\u044b \u0434\u043b\u044f \u0441\u0442\u0430\u0431\u0438\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f.<\/p>\n<p><strong>\u0427\u0442\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c\u043e \u0438 \u0434\u043b\u044f \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f, \u0438 \u0434\u043b\u044f \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 Flow Matching\u2019\u0430:<\/strong><\/p>\n<ul>\n<li>\n<p><strong>EMA<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u041d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u043c\u044b \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u0443\u0447\u0438\u043c \u043c\u043e\u0434\u0435\u043b\u044c, \u043c\u044b \u0441\u043e\u0445\u0440\u0430\u043d\u044f\u0435\u043c EMA-\u0432\u0435\u0440\u0441\u0438\u044e \u0438 \u0443\u0436\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0435\u0451.<\/p>\n<p><strong>EMA-\u0432\u0435\u0440\u0441\u0438\u044f \u043c\u043e\u0434\u0435\u043b\u0438<\/strong> \u2014 \u0441\u043a\u043e\u043b\u044c\u0437\u044f\u0449\u0435\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c \u043c\u043e\u0434\u0435\u043b\u0438. \u0418\u0437-\u0437\u0430 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043d\u0435\u0441\u0442\u0430\u0431\u0438\u043b\u044c\u043d\u043e, \u043c\u044b \u0431\u0435\u0440\u0451\u043c \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0445 \u0432\u0435\u0441\u043e\u0432 \u043c\u043e\u0434\u0435\u043b\u0438.<\/p>\n<p>\u042d\u0442\u043e \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u0430\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0430 \u0432 \u0441\u0432\u044f\u0437\u043a\u0435 \u0441 Adam\/AdamW, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0434\u0430\u0442 \u0441\u0442\u0430\u0431\u0438\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u0438 \u0441\u0438\u043b\u044c\u043d\u044b\u0439 \u043f\u0440\u0438\u0440\u043e\u0441\u0442 \u043a \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0443. \u0414\u043b\u044f \u043d\u0430\u0447\u0430\u043b\u0430 \u043c\u043e\u0436\u043d\u043e \u0432\u0437\u044f\u0442\u044c EMA = <strong>0.999-0.9999<\/strong>.<\/p>\n<ul>\n<li>\n<p><strong>Gradient clipping<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u0415\u0449\u0451 \u043e\u0434\u043d\u0430 \u0442\u0435\u0445\u043d\u0438\u043a\u0430 \u2014 \u043e\u0431\u0440\u0435\u0437\u043a\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043e\u0432. \u042d\u0442\u043e \u0437\u0430\u043c\u0435\u0442\u043d\u043e \u0443\u043b\u0443\u0447\u0448\u0430\u0435\u0442 \u0441\u0442\u0430\u0431\u0438\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043e\u043c. \u041d\u043e\u0440\u043c\u0443 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 \u0434\u043b\u044f \u043d\u0430\u0447\u0430\u043b\u0430 \u043c\u043e\u0436\u043d\u043e \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0438\u0442\u044c \u0435\u0434\u0438\u043d\u0438\u0446\u0435\u0439.<\/p>\n<ul>\n<li>\n<p><strong>Warmup<\/strong><\/p>\n<\/li>\n<\/ul>\n<p><strong>lr<\/strong> \u0443 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u043c\u043e\u0436\u043d\u043e \u0431\u0440\u0430\u0442\u044c \u043d\u0435 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u043c, \u0430 \u043d\u0430\u0447\u0438\u043d\u0430\u0442\u044c \u0441 \u043d\u0443\u043b\u044f \u0438 \u043f\u043e\u0442\u0438\u0445\u043e\u043d\u044c\u043a\u0443 \u043f\u043e\u0432\u044b\u0448\u0430\u0442\u044c \u0434\u043e \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0447\u0442\u043e\u0431\u044b \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0437\u043e\u0433\u043d\u0430\u043b\u043e\u0441\u044c \u0438 \u0441\u0442\u0430\u0431\u0438\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043b\u043e\u0441\u044c.<\/p>\n<p>Warmup \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u043e\u0431\u0435\u0438\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0438 \u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0442\u044c \u0447\u0438\u0441\u043b\u043e warmup \u0448\u0430\u0433\u043e\u0432 \u0438\u0437-\u0437\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"K\" alt=\"K\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg\" width=\"16\" height=\"12\" data-width=\"2.011\" data-height=\"1.545\" style=\"width: 2.011ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0447\u0442\u043e\u0431\u044b \u043e\u043d\u0438 \u0437\u0430\u043a\u043e\u043d\u0447\u0438\u043b\u0438 \u0435\u0433\u043e \u043e\u0434\u043d\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e.<\/p>\n<p>Warmup \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043d\u0430 <strong>5000<\/strong> \u0448\u0430\u0433\u043e\u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f. \u0423 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438 \u0431\u0430\u0437\u043e\u0432\u044b\u0439 <strong>lr<\/strong> = <strong>2e-4.<\/strong><\/p>\n<ul>\n<li>\n<p><strong>Dropout<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u041c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c, \u0447\u0442\u043e \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0448\u0430\u0433\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u044b \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u00ab\u0432\u044b\u043a\u043b\u044e\u0447\u0430\u0435\u043c\u00bb \u0447\u0430\u0441\u0442\u044c \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u043e\u0434\u0435\u043b\u044c \u0434\u043e\u043b\u0436\u043d\u0430 \u0440\u0435\u0448\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0443 \u0434\u0440\u0443\u0433\u0438\u043c \u043d\u0430\u0431\u043e\u0440\u043e\u043c \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432 \u0438 \u043d\u0435 \u043f\u0440\u0438\u0432\u044b\u043a\u0430\u0442\u044c \u043a \u043e\u0434\u043d\u043e\u043c\u0443 \u043f\u0443\u0442\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0439. \u042d\u0442\u043e \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u043a\u0430\u043a \u0440\u0435\u0433\u0443\u043b\u044f\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u043f\u043e\u043c\u043e\u0433\u0430\u0435\u0442 \u0431\u043e\u0440\u043e\u0442\u044c\u0441\u044f \u0441 \u043f\u0435\u0440\u0435\u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u043c.<\/p>\n<p>\u041f\u043e\u0437\u0436\u0435 \u043c\u044b \u043e\u0431\u0441\u0443\u0434\u0438\u043c, \u043f\u043e\u0447\u0435\u043c\u0443 \u044d\u0442\u043e \u043c\u043e\u0436\u0435\u0442 \u043d\u0435 \u0441\u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u043f\u0440\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>Dropout \u0434\u043b\u044f \u043d\u0430\u0447\u0430\u043b\u0430 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c <strong>0.0-0.2<\/strong>.<\/p>\n<ul>\n<li>\n<p><strong>\u0420\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f U-Net<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u041c\u043e\u0434\u0435\u043b\u044c U-Net (\u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043b\u0438 \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 <a href=\"https:\/\/arxiv.org\/pdf\/2509.22459\" rel=\"noopener nofollow\">RealUID<\/a>) \u043c\u043e\u0436\u043d\u043e \u0432\u0437\u044f\u0442\u044c \u0438\u0437 torchcfm. \u0412 \u044d\u0442\u043e\u043c \u0440\u0435\u043f\u043e\u0437\u0438\u0442\u043e\u0440\u0438\u0438 \u043f\u043e\u043d\u044f\u0442\u043d\u044b\u0439 \u043a\u043e\u0434, \u0435\u0441\u0442\u044c \u0432\u0435\u0441\u0430 \u043f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0434\u043b\u044f \u0440\u0430\u0437\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447.<\/p>\n<p>\u041f\u043e\u0434\u0440\u043e\u0431\u043d\u0435\u0435 \u043f\u0440\u043e U-Net \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0447\u0438\u0442\u0430\u0442\u044c <a href=\"https:\/\/nn.labml.ai\/unet\/index.html\" rel=\"noopener nofollow\">\u0442\u0443\u0442<\/a>.<\/p>\n<p><strong>\u0421\u043f\u0435\u0446\u0438\u0444\u0438\u0447\u043d\u044b\u0435 \u0434\u0435\u0442\u0430\u043b\u0438 \u0434\u043b\u044f \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438:<\/strong><\/p>\n<ul>\n<li>\n<p><strong>\u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u0415\u0441\u043b\u0438 \u043b\u0430\u0442\u0435\u043d\u0442\u043d\u044b\u0439 \u0448\u0443\u043c \u0438\u043c\u0435\u0435\u0442 \u0442\u0443 \u0436\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c, \u0447\u0442\u043e \u0438 \u0434\u0430\u043d\u043d\u044b\u0435, \u0442\u043e \u0435\u0441\u0442\u044c <img decoding=\"async\" class=\"formula inline\" source=\"m=d\" alt=\"m=d\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41c\/41c5d9fda6ce1ff816d0ab54c052f3a2.svg\" width=\"49\" height=\"14\" data-width=\"6.18\" data-height=\"1.756\" data-vertical-align=\"-0.186\" style=\"width: 6.18ex; height: 1.756ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41c\/41c5d9fda6ce1ff816d0ab54c052f3a2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41c\/41c5d9fda6ce1ff816d0ab54c052f3a2.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0443\u0434\u043e\u0431\u043d\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u0430\u043a <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi(z) = z + g_\\phi(z,0)\" alt=\"G_\\phi(z) = z + g_\\phi(z,0)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c0\/5c080a609356e3d85090dfdd65eaa198.svg\" width=\"158\" height=\"19\" data-width=\"19.737\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 19.737ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c0\/5c080a609356e3d85090dfdd65eaa198.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5c\/5c0\/5c080a609356e3d85090dfdd65eaa198.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043b\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi(z) = z + g_\\phi(z,\\tau)\" alt=\"G_\\phi(z) = z + g_\\phi(z,\\tau)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc5\/fc5caefc262497ccae2924fcc9d7d469.svg\" width=\"158\" height=\"19\" data-width=\"19.775\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 19.775ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc5\/fc5caefc262497ccae2924fcc9d7d469.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc5\/fc5caefc262497ccae2924fcc9d7d469.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0433\u0434\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"g_\\phi\" alt=\"g_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6317a7865929248bc6b1e3e0469bde.svg\" width=\"18\" height=\"19\" data-width=\"2.22\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.22ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6317a7865929248bc6b1e3e0469bde.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6317a7865929248bc6b1e3e0469bde.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c \u0442\u043e\u0439 \u0436\u0435 \u0430\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u044b, \u0447\u0442\u043e \u0438 \u043f\u043e\u043b\u0435 Flow Matching\u2019\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\theta\" alt=\"u_\\theta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg\" width=\"18\" height=\"18\" data-width=\"2.232\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.232ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/928\/9289b5573e49074225f6cddaf92ced0f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"\\tau\" alt=\"\\tau\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a6f\/a6f317b268ae825d94f832f970af607c.svg\" width=\"12\" height=\"18\" data-width=\"1.17\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.17ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a6f\/a6f317b268ae825d94f832f970af607c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a6\/a6f\/a6f317b268ae825d94f832f970af607c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043b\u044e\u0431\u044b\u043c. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"g_\\phi\" alt=\"g_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6317a7865929248bc6b1e3e0469bde.svg\" width=\"18\" height=\"19\" data-width=\"2.22\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.22ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6317a7865929248bc6b1e3e0469bde.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6317a7865929248bc6b1e3e0469bde.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u043c \u0432\u0435\u0441\u0430\u043c\u0438 \u043f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0439 Flow Matching-\u043c\u043e\u0434\u0435\u043b\u0438.<\/p>\n<p>\u0415\u0441\u043b\u0438 \u0436\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"m \\neq d\" alt=\"m \\neq d\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e43\/e434000bbe17a4f5a736acc7146dd66c.svg\" width=\"49\" height=\"18\" data-width=\"6.18\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.18ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e43\/e434000bbe17a4f5a736acc7146dd66c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e43\/e434000bbe17a4f5a736acc7146dd66c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0442\u0430\u043a\u0430\u044f \u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u0430\u044f \u0444\u043e\u0440\u043c\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"z+g_\\phi(z,0)\" alt=\"z+g_\\phi(z,0)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/925\/925528328eb18a9f55c74237c5bbceba.svg\" width=\"88\" height=\"19\" data-width=\"10.988\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 10.988ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/925\/925528328eb18a9f55c74237c5bbceba.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/925\/925528328eb18a9f55c74237c5bbceba.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0443\u0436\u0435 \u043d\u0435 \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442 \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"z\" alt=\"z\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg\" width=\"12\" height=\"12\" data-width=\"1.052\" data-height=\"1.025\" data-vertical-align=\"-0.025\" style=\"width: 1.052ex; height: 1.025ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fba\/fbade9e36a3f36d3d676c1b808451dd7.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi(z)\" alt=\"G_\\phi(z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg\" width=\"46\" height=\"19\" data-width=\"5.732\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 5.732ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a4\/a4b\/a4b9c02fb36e740ee0e65e7453edc0f0.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0436\u0438\u0432\u0443\u0442 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430\u0445 \u0440\u0430\u0437\u043d\u043e\u0439 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u2014 \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi : \\mathbb{R}^m \\to \\mathbb{R}^d\" alt=\"G_\\phi : \\mathbb{R}^m \\to \\mathbb{R}^d\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/32\/324\/324fa4cd187b0c8411958e284bba4792.svg\" width=\"114\" height=\"22\" data-width=\"14.204\" data-height=\"2.712\" data-vertical-align=\"-0.79\" style=\"width: 14.204ex; height: 2.712ex; vertical-align: -0.79ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/32\/324\/324fa4cd187b0c8411958e284bba4792.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/32\/324\/324fa4cd187b0c8411958e284bba4792.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<ul>\n<li>\n<p><strong>\u0418\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u0412\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0443\u0434\u043e\u0431\u043d\u043e \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0432\u0435\u0441\u0430\u043c\u0438 \u043f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f \u0443\u0447\u0438\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0412 \u043d\u0430\u0447\u0430\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0435\u0449\u0451 \u00ab\u043f\u043b\u043e\u0445\u043e\u0439\u00bb, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0442\u0430\u043a\u0430\u044f \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u044e \u0431\u043e\u043b\u0435\u0435 \u0441\u0442\u0430\u0431\u0438\u043b\u044c\u043d\u043e\u0439.<\/p>\n<p>\u0413\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0432\u0435\u0441\u0430\u043c\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<ul>\n<li>\n<p><strong>\u041e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u044b<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u0414\u043b\u044f \u043e\u0431\u0435\u0438\u0445 \u0441\u0435\u0442\u0435\u0439 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c Adam\/AdamW. \u0414\u043b\u044f \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0447\u0430\u0441\u0442\u043e \u043f\u043e\u043b\u0435\u0437\u043d\u043e \u043e\u0442\u043a\u043b\u044e\u0447\u0438\u0442\u044c \u043f\u0435\u0440\u0432\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442, \u0442\u043e \u0435\u0441\u0442\u044c \u0432\u0437\u044f\u0442\u044c Adam \u0441 <img decoding=\"async\" class=\"formula inline\" source=\"\\beta_1 = 0\" alt=\"\\beta_1 = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/583\/58371d417906f612461a0b6e167235cb.svg\" width=\"51\" height=\"18\" data-width=\"6.417\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.417ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/583\/58371d417906f612461a0b6e167235cb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/58\/583\/58371d417906f612461a0b6e167235cb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0414\u043b\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c Adam \u0441 <img decoding=\"async\" class=\"formula inline\" source=\"\\beta_1 \\ge 0\" alt=\"\\beta_1 \\ge 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f15\/f150a84a3869ca0550141fe6d8df1b62.svg\" width=\"51\" height=\"18\" data-width=\"6.417\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 6.417ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f15\/f150a84a3869ca0550141fe6d8df1b62.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f1\/f15\/f150a84a3869ca0550141fe6d8df1b62.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0422\u0430\u043a\u0430\u044f \u043d\u0430\u0441\u0442\u0440\u043e\u0439\u043a\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0432 \u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447\u0430\u0445, \u0433\u0434\u0435 \u043e\u0434\u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u044c \u0438\u0433\u0440\u0430\u0435\u0442 \u0440\u043e\u043b\u044c \u043a\u0440\u0438\u0442\u0438\u043a\u0430 \u0438\u043b\u0438 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f.<\/p>\n<p>\u0418\u043d\u0442\u0443\u0438\u0446\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f: <img decoding=\"async\" class=\"formula inline\" source=\"\\beta_1\" alt=\"\\beta_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b4c\/b4ceec2c4656f5c1e7fc76c59c4f80f3.svg\" width=\"18\" height=\"18\" data-width=\"2.268\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 2.268ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b4c\/b4ceec2c4656f5c1e7fc76c59c4f80f3.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b4\/b4c\/b4ceec2c4656f5c1e7fc76c59c4f80f3.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 momentum, \u0442\u043e \u0435\u0441\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438\u043d\u0435\u0440\u0446\u0438\u044f \u043f\u0440\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438. \u0418 \u0442\u0430\u043a \u043a\u0430\u043a \u0432\u043d\u0435\u0448\u043d\u044f\u044f \u0438\u0433\u0440\u0430 \u043e\u0447\u0435\u043d\u044c \u0441\u0438\u043b\u044c\u043d\u043e \u043c\u0435\u043d\u044f\u0435\u0442 \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u044e\u044e, \u0442\u043e \u044d\u0442\u0430 \u0438\u043d\u0435\u0440\u0446\u0438\u044f \u0431\u0443\u0434\u0435\u0442 \u043c\u0435\u0448\u0430\u0442\u044c, \u0442\u043e \u0435\u0441\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c Flow Matching \u043d\u0435 \u0443\u0441\u043f\u0435\u0435\u0442 \u0437\u0430 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u043e\u043c.<\/p>\n<p>\u0422\u0430\u043a\u0436\u0435 \u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043d\u0430\u0447\u0430\u043b\u0430 \u043e\u0442\u043a\u043b\u044e\u0447\u0430\u0442\u044c dropout \u0434\u043b\u044f \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u044d\u0442\u043e \u0437\u0430\u043c\u0435\u0434\u043b\u044f\u0435\u0442 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043c\u043e\u0434\u0435\u043b\u0438.<\/p>\n<ul>\n<li>\n<p><strong>\u041d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0448\u0430\u0433\u043e\u0432<\/strong> <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> <strong>\u043d\u0430 \u043e\u0434\u0438\u043d \u0448\u0430\u0433 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u041d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u043f\u043e\u043b\u0435\u0437\u043d\u043e \u0434\u0435\u043b\u0430\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0430 \u043e\u0434\u0438\u043d \u0448\u0430\u0433 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430. \u0420\u0430\u0431\u043e\u0447\u0435\u0435 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435: <img decoding=\"async\" class=\"formula inline\" source=\"K = 5\" alt=\"K = 5\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/72\/729\/7298db848934dbae09065631effd12bd.svg\" width=\"49\" height=\"14\" data-width=\"6.16\" data-height=\"1.731\" data-vertical-align=\"-0.186\" style=\"width: 6.16ex; height: 1.731ex; vertical-align: -0.186ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/72\/729\/7298db848934dbae09065631effd12bd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/72\/729\/7298db848934dbae09065631effd12bd.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0422\u043e \u0435\u0441\u0442\u044c \u0441\u043d\u0430\u0447\u0430\u043b\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"5\" alt=\"5\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4d\/e4da3b7fbbce2345d7772b0674a318d5.svg\" width=\"12\" height=\"12\" data-width=\"1.131\" data-height=\"1.557\" data-vertical-align=\"-0.05\" style=\"width: 1.131ex; height: 1.557ex; vertical-align: -0.05ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4d\/e4da3b7fbbce2345d7772b0674a318d5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e4\/e4d\/e4da3b7fbbce2345d7772b0674a318d5.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0440\u0430\u0437 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0430 \u0437\u0430\u0442\u0435\u043c \u043e\u0434\u0438\u043d \u0440\u0430\u0437 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u042d\u0442\u043e \u043f\u043e\u043c\u043e\u0433\u0430\u0435\u0442 \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u043c\u0443 \u043f\u043e\u043b\u044e \u043b\u0443\u0447\u0448\u0435 \u043e\u0442\u0441\u043b\u0435\u0436\u0438\u0432\u0430\u0442\u044c \u0442\u0435\u043a\u0443\u0449\u0435\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430.<\/p>\n<p>\u0422\u0430\u043a\u0436\u0435 \u0432\u043c\u0435\u0441\u0442\u0435 \u0441 <strong>K<\/strong> \u043c\u043e\u0436\u043d\u043e \u0430\u0434\u0430\u043f\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c <strong>lr<\/strong> \u0443 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0412\u043c\u0435\u0441\u0442\u0435 \u0441 <img decoding=\"async\" class=\"formula inline\" source=\"K\" alt=\"K\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg\" width=\"16\" height=\"12\" data-width=\"2.011\" data-height=\"1.545\" style=\"width: 2.011ex; height: 1.545ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u044d\u0442\u043e \u043f\u043e\u0437\u0432\u043e\u043b\u0438\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0443\u0441\u043f\u0435\u0432\u0430\u0442\u044c \u0443\u0447\u0438\u0442\u044c\u0441\u044f \u0437\u0430 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u043e\u043c.<\/p>\n<ul>\n<li>\n<p><strong>\u041d\u0438\u0437\u043a\u0430\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u0421\u0442\u043e\u0438\u0442 \u0441\u0442\u0430\u0432\u0438\u0442\u044c <strong>lr<\/strong> \u0443 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043f\u043e\u043c\u0435\u043d\u044c\u0448\u0435 (\u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <strong>3e-5<\/strong>), \u0438\u043d\u0430\u0447\u0435 \u043e\u043d \u0431\u0443\u0434\u0435\u0442 \u0443\u0447\u0438\u0442\u044c\u0441\u044f \u043d\u0435\u0441\u0442\u0430\u0431\u0438\u043b\u044c\u043d\u043e \u0438\u0437-\u0437\u0430 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u043b\u043e\u0441\u0441\u0430.<\/p>\n<p>\u041f\u0440\u0438 \u044d\u0442\u043e\u043c <strong>lr<\/strong> \u0443 \u0444\u0435\u0439\u043a-\u043c\u043e\u0434\u0435\u043b\u0438 \u043c\u043e\u0436\u043d\u043e \u0431\u0440\u0430\u0442\u044c \u043a\u0430\u043a <strong>3e-5<\/strong>, \u0442\u0430\u043a \u0438 <strong>2e-4<\/strong>. \u041e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0433\u0438\u043f\u0435\u0440\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u043c\u043e\u0436\u043d\u043e \u0432\u0437\u044f\u0442\u044c \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u0435.<\/p>\n<ul>\n<li>\n<p><strong>\u0417\u0430\u043c\u043e\u0440\u043e\u0437\u043a\u0430 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0438 stop-gradient<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u041e\u0447\u0435\u043d\u044c \u0432\u0430\u0436\u043d\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u044f\u0442\u044c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430\u043c\u0438. \u041a\u043e\u0433\u0434\u0430 \u043c\u044b \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0442\u0435\u043a\u0443\u0449\u0438\u0445 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430 \u044d\u0442\u043e\u043c \u0448\u0430\u0433\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043d\u0435 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u044e\u0442\u0441\u044f: <code>G_phi.eval()<\/code>, <code>G_phi.requires_grad_(False)<\/code>. \u0412\u044b\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u043c\u043e\u0436\u043d\u043e \u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0441\u043e stop-gradient: <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_1 = \\operatorname{stopgrad}(G_\\phi(z))\" alt=\"\\hat{x}_1 = \\operatorname{stopgrad}(G_\\phi(z))\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4b\/f4b47afe3d78ab20234d5405052ecbb0.svg\" width=\"171\" height=\"20\" data-width=\"21.359\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 21.359ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4b\/f4b47afe3d78ab20234d5405052ecbb0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f4\/f4b\/f4b47afe3d78ab20234d5405052ecbb0.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0432 PyTorch \u044d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0447\u0435\u0440\u0435\u0437 <code>torch.no_grad()<\/code> \u0438\u043b\u0438 <code>.detach()<\/code>. \u041a\u043e\u0433\u0434\u0430 \u043c\u044b \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442, \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0437\u0430\u043c\u043e\u0440\u0430\u0436\u0438\u0432\u0430\u044e\u0442\u0441\u044f:  <code>u_psi.eval()<\/code>, <code>u_psi.requires_grad_(False)<\/code>,  <code>u_star.eval()<\/code>, <code>u_star.requires_grad_(False)<\/code>.<\/p>\n<p>\u041d\u043e \u0437\u0434\u0435\u0441\u044c \u043d\u0435\u043b\u044c\u0437\u044f \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c <code>torch.no_grad()<\/code> \u0432\u043e\u043a\u0440\u0443\u0433 <img decoding=\"async\" class=\"formula inline\" source=\"u^*(\\hat{x}_t,t)\" alt=\"u^*(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg\" width=\"63\" height=\"19\" data-width=\"7.924\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 7.924ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/53\/533\/5332cf0968731663776fa7861fed788c.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi(\\hat{x}_t,t)\" alt=\"u_\\psi(\\hat{x}_t,t)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg\" width=\"65\" height=\"20\" data-width=\"8.166\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 8.166ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0a\/0a8\/0a85bbde7df7efa60693e2639622ce68.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0434\u0435\u043b\u0430\u0442\u044c <code>x_t_hat.detach()<\/code>. \u041f\u0440\u0438\u0447\u0438\u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f: \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 <img decoding=\"async\" class=\"formula inline\" source=\"u_\\psi\" alt=\"u_\\psi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg\" width=\"20\" height=\"19\" data-width=\"2.523\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.523ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/05\/058\/05809fab71448bcbe6ec9a0655ee73eb.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0435 \u0434\u043e\u043b\u0436\u043d\u044b \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0442\u044c\u0441\u044f, \u043d\u043e \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0443 \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442\u044c \u0447\u0435\u0440\u0435\u0437 \u0438\u0445 \u0432\u0445\u043e\u0434 <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t\" alt=\"\\hat{x}_t\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg\" width=\"16\" height=\"19\" data-width=\"2.059\" data-height=\"2.398\" data-vertical-align=\"-0.633\" style=\"width: 2.059ex; height: 2.398ex; vertical-align: -0.633ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/41\/41e\/41ef26b74bdb937679d28b1f84087514.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\hat{x}_t = (1-t)x_0 + tG_\\phi(z)\" alt=\"\\hat{x}_t = (1-t)x_0 + tG_\\phi(z)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/75\/757\/7570e4a071abe5b1903593588976e8c5.svg\" width=\"185\" height=\"20\" data-width=\"23.146\" data-height=\"2.5\" data-vertical-align=\"-0.684\" style=\"width: 23.146ex; height: 2.5ex; vertical-align: -0.684ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/75\/757\/7570e4a071abe5b1903593588976e8c5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/75\/757\/7570e4a071abe5b1903593588976e8c5.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430. \u0415\u0441\u043b\u0438 \u043e\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u044c \u044d\u0442\u043e\u0442 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442, \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u0442 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u0439 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u0439 \u0441\u0438\u0433\u043d\u0430\u043b.<\/p>\n<ul>\n<li>\n<p><strong>\u041f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430\u044f \u0444\u0438\u043a\u0441\u0430\u0446\u0438\u044f \u0443\u0447\u0438\u0442\u0435\u043b\u044f<\/strong><\/p>\n<\/li>\n<\/ul>\n<p>\u041f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"u^*\" alt=\"u^*\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg\" width=\"18\" height=\"14\" data-width=\"2.282\" data-height=\"1.703\" data-vertical-align=\"-0.025\" style=\"width: 2.282ex; height: 1.703ex; vertical-align: -0.025ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/94b\/94b5e62c10e98ca055cca773caed8668.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432\u043e \u0432\u0440\u0435\u043c\u044f \u0432\u0441\u0435\u0439 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 \u043e\u0441\u0442\u0430\u0451\u0442\u0441\u044f \u0432 \u0440\u0435\u0436\u0438\u043c\u0435 <code>eval<\/code> \u0438 \u043d\u0435 \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u0435\u0442\u0441\u044f. \u041e\u043d\u043e \u0438\u0433\u0440\u0430\u0435\u0442 \u0440\u043e\u043b\u044c \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e \u0443\u0447\u0438\u0442\u0435\u043b\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0437\u0430\u0434\u0430\u0451\u0442 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u043e\u0442 \u0448\u0443\u043c\u0430 \u043a \u0434\u0430\u043d\u043d\u044b\u043c.<\/p>\n<\/div>\n<\/details>\n<h3>\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f<\/h3>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0438 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 Flow Matching-\u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430 \u0434\u0430\u0442\u0430\u0441\u0435\u0442\u0435 CIFAR-10 \u2014 \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0438 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c 32 \u0445 32 \u043f\u0438\u043a\u0441\u0435\u043b\u044f. \u0412\u0441\u0435\u0433\u043e \u0435\u0441\u0442\u044c 10 \u0440\u0430\u0437\u043d\u044b\u0445 \u043a\u043b\u0430\u0441\u0441\u043e\u0432 \u2014 \u0441\u0430\u043c\u043e\u043b\u0451\u0442\u044b, \u043c\u0430\u0448\u0438\u043d\u044b, \u043f\u0442\u0438\u0446\u044b \u0438 \u0434\u0440.<\/p>\n<p>\u0427\u0442\u043e\u0431\u044b \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0445\u043e\u0440\u043e\u0448\u043e, \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043c\u0435\u0442\u0440\u0438\u043a\u0443 <strong>FID (Fr\u00e9chet Inception Distance)<\/strong> \u2014 \u043e\u043d\u0430 \u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u0442 \u043d\u0430\u0431\u043e\u0440 \u0444\u043e\u0442\u043e \u0441 \u043d\u0430\u0431\u043e\u0440\u043e\u043c \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043a\u0430\u0440\u0442\u0438\u043d\u043e\u043a. \u0427\u0435\u043c \u043d\u0430\u0431\u043e\u0440\u044b \u043a\u0430\u0440\u0442\u0438\u043d\u043e\u043a \u0431\u043b\u0438\u0436\u0435, \u0442\u0435\u043c \u043b\u0443\u0447\u0448\u0435.<\/p>\n<details class=\"spoiler\">\n<summary>FID-\u043c\u0435\u0442\u0440\u0438\u043a\u0430<\/summary>\n<div class=\"spoiler__content\">\n<p>\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u043e \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044e <img decoding=\"async\" class=\"formula inline\" source=\"x_i\" alt=\"x_i\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1ba\/1ba8aaab47179b3d3e24b0ccea9f4e30.svg\" width=\"16\" height=\"12\" data-width=\"2.034\" data-height=\"1.357\" data-vertical-align=\"-0.357\" style=\"width: 2.034ex; height: 1.357ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1ba\/1ba8aaab47179b3d3e24b0ccea9f4e30.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1b\/1ba\/1ba8aaab47179b3d3e24b0ccea9f4e30.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0437 \u043f\u0440\u0435\u0434\u043e\u0431\u0443\u0447\u0435\u043d\u043d\u043e\u0439 \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u0438 (\u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, Inception-v3) \u0438\u0437\u0432\u043b\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u0447\u0438\u0441\u043b\u043e\u0432\u044b\u0435 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"h_i\" alt=\"h_i\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/57\/573\/57339b77b3af15427b7154f4daf8a223.svg\" width=\"16\" height=\"15\" data-width=\"2.043\" data-height=\"1.927\" data-vertical-align=\"-0.357\" style=\"width: 2.043ex; height: 1.927ex; vertical-align: -0.357ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/57\/573\/57339b77b3af15427b7154f4daf8a223.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/57\/573\/57339b77b3af15427b7154f4daf8a223.svg 781w\" loading=\"lazy\" decode=\"async\"\/>. \u0417\u0430\u0442\u0435\u043c \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u044d\u0442\u0438 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0438 \u043a\u0430\u043a \u043d\u0430 \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0438\u0437 \u043c\u043d\u043e\u0433\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f. \u041f\u0440\u0438 \u044d\u0442\u043e\u043c, \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0438 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0438 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043a\u0430\u0440\u0442\u0438\u043d\u043e\u043a \u0441\u0435\u043c\u043f\u043b\u0438\u0440\u0443\u044e\u0442\u0441\u044f \u0438\u0437 \u0434\u0432\u0443\u0445 \u0440\u0430\u0437\u043d\u044b\u0445 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439: <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{N(\\mu, \\Sigma)}\" alt=\"\\mathcal{N(\\mu, \\Sigma)}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/df\/dff\/dff4e030703d1ebe797ac0ee2291c911.svg\" width=\"69\" height=\"19\" data-width=\"8.569\" data-height=\"2.351\" data-vertical-align=\"-0.61\" style=\"width: 8.569ex; height: 2.351ex; vertical-align: -0.61ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/df\/dff\/dff4e030703d1ebe797ac0ee2291c911.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/d\/df\/dff\/dff4e030703d1ebe797ac0ee2291c911.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438  <img decoding=\"async\" class=\"formula inline\" source=\"\\mathcal{N(\\hat{\\mu}, \\hat{\\Sigma})}\" alt=\"\\mathcal{N(\\hat{\\mu}, \\hat{\\Sigma})}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a31\/a31dc2060e58a557cf765577d04249fe.svg\" width=\"69\" height=\"24\" data-width=\"8.569\" data-height=\"2.952\" data-vertical-align=\"-0.911\" style=\"width: 8.569ex; height: 2.952ex; vertical-align: -0.911ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a31\/a31dc2060e58a557cf765577d04249fe.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a31\/a31dc2060e58a557cf765577d04249fe.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0414\u043b\u044f \u0434\u0432\u0443\u0445 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u043c\u044b \u0437\u043d\u0430\u0435\u043c \u043c\u0435\u0442\u0440\u0438\u043a\u0443: <img decoding=\"async\" class=\"formula inline\" source=\"d_F\\left(\\mathcal{N}(\\mu,\\Sigma),\\mathcal{N}(\\hat{\\mu},\\hat{\\Sigma})\\right)^2=\\left\\|\\mu-\\hat{\\mu}\\right\\|_2^2+\\operatorname{tr}\\left(\\Sigma+\\hat{\\Sigma}-2\\left(\\Sigma\\hat{\\Sigma}\\right)^{\\frac{1}{2}}\\right)\" alt=\"d_F\\left(\\mathcal{N}(\\mu,\\Sigma),\\mathcal{N}(\\hat{\\mu},\\hat{\\Sigma})\\right)^2=\\left\\|\\mu-\\hat{\\mu}\\right\\|_2^2+\\operatorname{tr}\\left(\\Sigma+\\hat{\\Sigma}-2\\left(\\Sigma\\hat{\\Sigma}\\right)^{\\frac{1}{2}}\\right)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8e\/8e5\/8e5ca3eae7520261fc9e481b3b19afe4.svg\" width=\"487\" height=\"44\" data-width=\"60.825\" data-height=\"5.515\" data-vertical-align=\"-2.192\" style=\"width: 60.825ex; height: 5.515ex; vertical-align: -2.192ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8e\/8e5\/8e5ca3eae7520261fc9e481b3b19afe4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8e\/8e5\/8e5ca3eae7520261fc9e481b3b19afe4.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0421\u0440\u0435\u0434\u043d\u0435\u0435 \u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u043a\u043e\u0432\u0430\u0440\u0438\u0430\u0446\u0438\u0439 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043c\u043e\u0436\u043d\u043e \u043e\u0446\u0435\u043d\u0438\u0442\u044c \u043f\u043e \u0441\u0435\u043c\u043f\u043b\u0430\u043c: <img decoding=\"async\" class=\"formula inline\" source=\"\\mu\" alt=\"\\mu\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c9f\/c9faf6ead2cd2c2187bd943488de1d0a.svg\" width=\"12\" height=\"18\" data-width=\"1.364\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 1.364ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c9f\/c9faf6ead2cd2c2187bd943488de1d0a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c9f\/c9faf6ead2cd2c2187bd943488de1d0a.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u0441\u0435\u043c\u043f\u043b\u043e\u0432, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u043a\u043e\u0432\u0430\u0440\u0438\u0430\u0446\u0438\u0438 \u2014 \u0447\u0435\u0440\u0435\u0437 <img decoding=\"async\" class=\"formula inline\" source=\"\\Sigma=\\frac{1}{N-1}(X-\\mathbf{1}\\mu)^T(X-\\mathbf{1}\\mu)\" alt=\"\\Sigma=\\frac{1}{N-1}(X-\\mathbf{1}\\mu)^T(X-\\mathbf{1}\\mu)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b2f\/b2ffcc005ad326bb4c0c7744de7073a9.svg\" width=\"249\" height=\"38\" data-width=\"31.103\" data-height=\"4.774\" data-vertical-align=\"-1.821\" style=\"width: 31.103ex; height: 4.774ex; vertical-align: -1.821ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b2f\/b2ffcc005ad326bb4c0c7744de7073a9.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b2f\/b2ffcc005ad326bb4c0c7744de7073a9.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<\/div>\n<\/details>\n<p>\u0412 \u0441\u0442\u0430\u0442\u044c\u0435 <a href=\"https:\/\/arxiv.org\/pdf\/2509.22459\" rel=\"noopener nofollow\">RealUID<\/a> FID \u0434\u043b\u044f Flow Matching\u2019\u0430 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u0440\u0430\u0432\u043d\u044b\u043c <strong>3.57<\/strong> \u043d\u0430 100 \u0448\u0430\u0433\u0430\u0445 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u0438 \u044d\u0442\u043e\u043c \u043f\u043e\u0441\u043b\u0435 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 FID \u0443\u043c\u0435\u043d\u044c\u0448\u0438\u043b\u0441\u044f \u0434\u043e <strong>2.58<\/strong>. \u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0432 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0437 \u0443\u0441\u043a\u043e\u0440\u044f\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044e (1 \u0448\u0430\u0433 \u0432\u043c\u0435\u0441\u0442\u043e 100), \u043d\u043e \u0438 \u0443\u043b\u0443\u0447\u0448\u0430\u0435\u043c \u0435\u0451 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e.<\/p>\n<p>\u041c\u044b \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438\u0437 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430 CIFAR-10, \u0447\u0442\u043e\u0431\u044b \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/160\/74c\/8a7\/16074c8a7616f711635dd11eb087f2bc.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 29. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438, \u0432\u044b\u0443\u0447\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 CIFAR-10\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/160\/74c\/8a7\/16074c8a7616f711635dd11eb087f2bc.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/160\/74c\/8a7\/16074c8a7616f711635dd11eb087f2bc.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 29. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438, \u0432\u044b\u0443\u0447\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 CIFAR-10<\/figcaption><\/div>\n<\/figure>\n<p>\u0422\u0430\u043a\u0436\u0435 \u043f\u0440\u0438\u0432\u0435\u0434\u0451\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u043b\u0438\u0446 \u043d\u0430 \u0434\u0430\u0442\u0430\u0441\u0435\u0442\u0435 CelebA \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c 64 \u0445 64:<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/cbd\/e7c\/794\/cbde7c794ccdd0adff2bd2067382b747.png\" alt=\"\u0420\u0438\u0441\u0443\u043d\u043e\u043a 30. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438, \u0432\u044b\u0443\u0447\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 CelebA\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/cbd\/e7c\/794\/cbde7c794ccdd0adff2bd2067382b747.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/cbd\/e7c\/794\/cbde7c794ccdd0adff2bd2067382b747.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 30. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438, \u0432\u044b\u0443\u0447\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 CelebA<\/figcaption><\/div>\n<\/figure>\n<h3>\u0417\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435<\/h3>\n<p>\u0418\u0442\u0430\u043a, \u0432 \u044d\u0442\u043e\u043c \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438, \u043a\u0430\u043a \u0443\u0441\u0442\u0440\u043e\u0435\u043d Flow Matching \u2014 \u043f\u0435\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u0448\u0443\u043c\u0430 \u043a \u0434\u0430\u043d\u043d\u044b\u043c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0435\u0439.<\/p>\n<p>\u041c\u044b \u043e\u0431\u0441\u0443\u0434\u0438\u043b\u0438 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043d\u0435\u0434\u043e\u0441\u0442\u0430\u0442\u043e\u043a: \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044f \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0433\u043e \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u2014 \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043e\u0434\u043d\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043d\u0443\u0436\u043d\u043e \u043c\u043d\u043e\u0433\u043e \u0440\u0430\u0437 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0441\u0442\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f.<\/p>\n<p>\u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u0438\u0434\u0435\u044e \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438: \u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u0443\u044e \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044e \u043e\u0434\u043d\u0438\u043c \u0437\u0430\u043f\u0443\u0441\u043a\u043e\u043c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"G_\\phi\" alt=\"G_\\phi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg\" width=\"23\" height=\"19\" data-width=\"2.92\" data-height=\"2.364\" data-vertical-align=\"-0.616\" style=\"width: 2.92ex; height: 2.364ex; vertical-align: -0.616ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/ea7\/ea79b75e8dfd968b3461021891dcc703.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u0431\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e <img decoding=\"async\" class=\"formula inline\" source=\"\\min\\max\" alt=\"\\min\\max\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/395\/3952285ad4c49df77902e0f8f370ee04.svg\" width=\"67\" height=\"18\" data-width=\"8.359\" data-height=\"2.262\" data-vertical-align=\"-0.566\" style=\"width: 8.359ex; height: 2.262ex; vertical-align: -0.566ex\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/395\/3952285ad4c49df77902e0f8f370ee04.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/395\/3952285ad4c49df77902e0f8f370ee04.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u0433\u0440\u044b. \u0412 \u0438\u0442\u043e\u0433\u0435 \u043c\u044b \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0443\u0441\u043a\u043e\u0440\u0438\u043b\u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044e, \u043d\u043e \u0438 \u0443\u043b\u0443\u0447\u0448\u0438\u043b\u0438 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e \u043a\u0430\u0440\u0442\u0438\u043d\u043e\u043a.<\/p>\n<h3>\u041f\u043e\u043b\u0435\u0437\u043d\u044b\u0435 \u0441\u0441\u044b\u043b\u043a\u0438<\/h3>\n<ol>\n<li>\n<p>\u0421\u0442\u0430\u0442\u044c\u044f \u043f\u0440\u043e <a href=\"https:\/\/arxiv.org\/pdf\/2210.02747\" rel=\"noopener nofollow\">Flow Matching<\/a>.<\/p>\n<\/li>\n<li>\n<p>\u0421\u0442\u0430\u0442\u044c\u044f \u043f\u0440\u043e <a href=\"https:\/\/arxiv.org\/pdf\/2305.16860\" rel=\"noopener nofollow\">\u043e\u0448\u0438\u0431\u043a\u0443, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u0442 Flow Matching<\/a>.<\/p>\n<\/li>\n<li>\n<p>TorchCFM \u2014 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f Flow Matching\u2019\u0430.<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/pdf\/2404.04057\" rel=\"noopener nofollow\">SiD<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2311.18828\" rel=\"noopener nofollow\">DMD<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2410.19310\" rel=\"noopener nofollow\">FGM<\/a> \u2014 \u043c\u0435\u0442\u043e\u0434\u044b \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438.<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/pdf\/1406.2661\" rel=\"noopener nofollow\">GAN<\/a> \u043a\u0430\u043a min-max \u0438\u0433\u0440\u0430.<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/pdf\/2509.22459\" rel=\"noopener nofollow\">RealUID<\/a>, <a href=\"https:\/\/github.com\/David-cripto\/RealUID\" rel=\"noopener nofollow\">code<\/a> \u2014 \u043d\u0430\u0448\u0430 \u0441\u0442\u0430\u0442\u044c\u044f \u043f\u0440\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0435\u0442\u043e\u0434 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 \u0441 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0434\u0430\u043d\u043d\u044b\u043c\u0438 + \u043a\u043e\u0434 \u043a \u043d\u0435\u0439.<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/pdf\/2303.01469\" rel=\"noopener nofollow\">Consistency models<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2507.03738\" rel=\"noopener nofollow\">FACM<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2602.17682\" rel=\"noopener nofollow\">DuMo<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2505.13447\" rel=\"noopener nofollow\">MeanFlow<\/a>, \u03c0-Flow, <a href=\"https:\/\/arxiv.org\/pdf\/2403.12015\" rel=\"noopener nofollow\">LADD<\/a> \u2014 \u0434\u0440\u0443\u0433\u0438\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 \u0438 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0432 \u043e\u0434\u0438\u043d \u0438\u043b\u0438 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0448\u0430\u0433\u043e\u0432.<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/pdf\/2209.03003\" rel=\"noopener nofollow\">Rectified Flows<\/a> \u2014 \u0438\u043d\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0443\u0441\u043a\u043e\u0440\u0438\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044e Flow Matching\u2019\u0430.<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/diffusionflow.github.io\" rel=\"noopener nofollow\">Diffusion Meets Flow Matching<\/a> \u2014 \u043f\u043e\u0441\u0442 \u043f\u0440\u043e \u0441\u0432\u044f\u0437\u044c \u0434\u0438\u0444\u0444\u0443\u0437\u0438\u043e\u043d\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0438 flow matching\u2019\u0430.<\/p>\n<\/li>\n<li>\n<p>DDPM, Score-Based Generative Modeling through Stochastic Differential Equations \u2014 \u043f\u0440\u043e \u0434\u0438\u0444\u0444\u0443\u0437\u0438\u043e\u043d\u043d\u044b\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 (\u0441\u0438\u043b\u044c\u043d\u043e \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0441 Flow Matching\u2019\u043e\u043c).<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/pdf\/1312.6114\" rel=\"noopener nofollow\">VAE<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/1602.02282\" rel=\"noopener nofollow\">LVAE<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2011.10650\" rel=\"noopener nofollow\">VDVAE<\/a>, NCSN, Deep Unsupervised Learning using Nonequilibrium Thermodynamics, <a href=\"https:\/\/arxiv.org\/pdf\/2107.00630\" rel=\"noopener nofollow\">Variational Diffusion Models<\/a>, <a href=\"https:\/\/arxiv.org\/abs\/2112.10752\" rel=\"noopener nofollow\">Latent Diffusion<\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2404.12940\" rel=\"noopener nofollow\">NFDM<\/a> \u2014 \u0434\u043b\u044f \u043b\u0443\u0447\u0448\u0435\u0433\u043e \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0434\u0438\u0444\u0444\u0443\u0437\u0438\u043e\u043d\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 (\u0442\u0440\u0438 \u0432\u0437\u0433\u043b\u044f\u0434\u0430 \u043d\u0430 \u043d\u0438\u0445 \u2014 variational, score \u0438 flow).<\/p>\n<\/li>\n<li>\n<p>\u0421\u0442\u0430\u0442\u044c\u044f \u043f\u0440\u043e <a href=\"https:\/\/arxiv.org\/pdf\/1806.07366\" rel=\"noopener nofollow\">continuous normalizing flows<\/a> (\u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043c\u043e\u0447\u044c \u043b\u0443\u0447\u0448\u0435 \u043f\u043e\u043d\u044f\u0442\u044c Flow Matching).<\/p>\n<\/li>\n<li>\n<p>\u041b\u0435\u043a\u0446\u0438\u0438 BayesGroup \u043f\u043e continuous normalizing flows \u0438 \u0434\u0438\u0444\u0444\u0443\u0437\u0438\u043e\u043d\u043d\u044b\u043c \u043c\u043e\u0434\u0435\u043b\u044f\u043c.<\/p>\n<\/li>\n<li>\n<p>The Annotated Transformer \u2014 \u0434\u043b\u044f \u043b\u0443\u0447\u0448\u0435\u0433\u043e \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0443\u0441\u0442\u0440\u043e\u0439\u0441\u0442\u0432\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439.<\/p>\n<\/li>\n<li>\n<p><a href=\"http:\/\/nn.labml.ai\/\" rel=\"noopener nofollow\">nn.labml.ai<\/a> \u2014 \u0434\u043b\u044f \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u043c\u0430\u0448\u0438\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f, \u0432 \u0442\u043e\u043c \u0447\u0438\u0441\u043b\u0435 \u2014 U-Net, Stable Diffusion.<\/p>\n<\/li>\n<\/ol>\n<h3>\u041f\u043e\u043b\u0435\u0437\u043d\u044b\u0435 \u0441\u0441\u044b\u043b\u043a\u0438 \u043d\u0430 \u043f\u043e\u0441\u0442\u044b DeepSchool<\/h3>\n<ol>\n<li>\n<p><a href=\"https:\/\/blog.deepschool.ru\/cv\/gencv\/distillyacziya-diffuzii-chast-1\/\" rel=\"noopener nofollow\">\u041f\u043e\u0441\u0442 1<\/a> \u0438 <a href=\"https:\/\/blog.deepschool.ru\/cv\/gencv\/distillyacziya-diffuzii-chast-2\/\" rel=\"noopener nofollow\">\u043f\u043e\u0441\u0442 2<\/a> \u043f\u0440\u043e \u0434\u0438\u0441\u0442\u0438\u043b\u044f\u0446\u0438\u044e \u0434\u0438\u0444\u0444\u0443\u0437\u0438\u0438<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/blog.deepschool.ru\/cv\/gencv\/consistency-models\/\" rel=\"noopener nofollow\">Consistency models<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/blog.deepschool.ru\/cv\/gencv\/instaflow-2\/\" rel=\"noopener nofollow\">\u041f\u0440\u043e Rectified Flows \u0438 InstaFlow<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/blog.deepschool.ru\/cv\/vvedenie-v-diffuzionnye-modeli\/\" rel=\"noopener nofollow\">\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0434\u0438\u0444\u0444\u0443\u0437\u0438\u043e\u043d\u043d\u044b\u0435 \u043c\u043e\u0434\u0435\u043b\u0438<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/blog.deepschool.ru\/cv\/genie-family\/\" rel=\"noopener nofollow\">\u041f\u0440\u043e \u043c\u043e\u0434\u0435\u043b\u0438 Genie<\/a><\/p>\n<\/li>\n<\/ol>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/482\/fe2\/7b1\/482fe27b13eb95a2fab26c10f427e64f.png\" sizes=\"(max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/\/post_images\/482\/fe2\/7b1\/482fe27b13eb95a2fab26c10f427e64f.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/\/post_images\/482\/fe2\/7b1\/482fe27b13eb95a2fab26c10f427e64f.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/figure>\n<\/div>\n<p>\u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/articles\/1087486\/\">https:\/\/habr.com\/ru\/articles\/1087486\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0420\u0438\u0441\u0443\u043d\u043e\u043a 1. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0435\u0439 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439: \u0438\u0437 \u0448\u0443\u043c\u0430 \u043f\u043e\u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0432\u0438\u0434\u0435\u043e, \u0437\u0432\u0443\u043a \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0435 \u043e\u0431\u044a\u0435\u043a\u0442\u044bFlow Matching \u2014 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0439 \u043f\u043e\u0434\u0445\u043e\u0434 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f. \u041e\u0441\u043d\u043e\u0432\u043d\u0430\u044f \u0438\u0434\u0435\u044f \u2014 \u043d\u0430\u0443\u0447\u0438\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u043e\u0441\u0442\u0435\u043f\u0435\u043d\u043d\u043e \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u0448\u0443\u043c, \u0432 \u0441\u043b\u043e\u0436\u043d\u044b\u0435 \u0434\u0430\u043d\u043d\u044b\u0435 \u2014 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0432\u0438\u0434\u0435\u043e, \u0437\u0432\u0443\u043a, 3D-\u0441\u0446\u0435\u043d\u044b \u0438\u043b\u0438 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u0440\u043e\u0431\u043e\u0442\u0430.\u0412 \u0440\u0430\u043c\u043a\u0430\u0445 \u0441\u0442\u0430\u0442\u044c\u0438 \u0440\u0430\u0437\u0431\u0435\u0440\u0451\u043c \u0443\u0441\u0442\u0440\u043e\u0439\u0441\u0442\u0432\u043e Flow Matching\u2019\u0430: \u043a\u0430\u043a \u0437\u0430\u0434\u0430\u0451\u0442\u0441\u044f \u043f\u0443\u0442\u044c \u043e\u0442 \u0448\u0443\u043c\u0430 \u043a \u0434\u0430\u043d\u043d\u044b\u043c, \u0447\u0435\u043c\u0443 \u0443\u0447\u0438\u0442\u0441\u044f \u043c\u043e\u0434\u0435\u043b\u044c \u0438 \u043a\u0430\u043a \u043f\u043e\u0441\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0438\u0437 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0433\u043e \u0448\u0443\u043c\u0430 \u043f\u043e\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u043e\u0432\u044b\u0439 \u043e\u0431\u044a\u0435\u043a\u0442. \u041e\u0431\u0441\u0443\u0434\u0438\u043c \u0433\u043b\u0430\u0432\u043d\u044b\u0439 \u043d\u0435\u0434\u043e\u0441\u0442\u0430\u0442\u043e\u043a \u043f\u043e\u0434\u0445\u043e\u0434\u0430 \u2014 \u043c\u0435\u0434\u043b\u0435\u043d\u043d\u0430\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u044f (\u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043e\u0434\u0438\u043d \u043e\u0431\u044a\u0435\u043a\u0442, \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u043c\u043d\u043e\u0433\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0448\u0430\u0433\u043e\u0432).\u041e\u0434\u0438\u043d \u0438\u0437 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0435\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u2014 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u044f. \u041c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043c \u043c\u043d\u043e\u0433\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u043e\u043c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0437\u0430 \u043e\u0434\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0451\u0442 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u044b\u0435 \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0438.\u041e\u0434\u043d\u0430\u043a\u043e \u0442\u0430\u043a\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c \u043d\u0435\u043b\u044c\u0437\u044f \u043f\u0440\u043e\u0441\u0442\u043e \u043e\u0431\u0443\u0447\u0438\u0442\u044c \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0435\u0439 \u043f\u043e \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0443: \u00ab\u0412\u043e\u0442 \u2014 \u0432\u0445\u043e\u0434, \u0432\u043e\u0442 \u2014 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u0439 \u043e\u0442\u0432\u0435\u0442\u00bb. \u041c\u044b \u0440\u0430\u0437\u0431\u0435\u0440\u0451\u043c, \u043f\u043e\u0447\u0435\u043c\u0443 \u044d\u0442\u043e \u0442\u0430\u043a \u0438 \u043a\u0430\u043a \u0438\u0437 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u0438\u0441\u0442\u0438\u043b\u043b\u044f\u0446\u0438\u0438 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442\u00a0\u043c\u0438\u043d\u0438\u043c\u0430\u043a\u0441\u043d\u0430\u044f \u043f\u043e\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430: \u0434\u0432\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430\u0447\u0438\u043d\u0430\u044e\u0442 \u0438\u0433\u0440\u0430\u0442\u044c \u0434\u0440\u0443\u0433 \u0441 \u0434\u0440\u0443\u0433\u043e\u043c, \u0430 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u0438\u0433\u0440\u044b \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c!\u0421\u0444\u0435\u0440\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044fFlow Matching \u0441\u0435\u0433\u043e\u0434\u043d\u044f \u2014 \u043e\u0434\u0438\u043d \u0438\u0437 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0445 \u043f\u043e\u0434\u0445\u043e\u0434\u043e\u0432 \u0432 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u044f\u0445, \u00ab\u0440\u0430\u0432\u043d\u044b\u0439\u00bb \u0434\u0438\u0444\u0444\u0443\u0437\u0438\u043e\u043d\u043d\u044b\u043c \u043c\u043e\u0434\u0435\u043b\u044f\u043c (\u0432 \u043a\u0430\u043a\u043e\u043c-\u0442\u043e \u0441\u043c\u044b\u0441\u043b\u0435 \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u044d\u0442\u043e \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435).\u0418\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u2014 Stable Diffusion 3.5, FLUX.2 \u0438 Kandinsky \u043e\u0442 \u0421\u0431\u0435\u0440\u0430. \u042d\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u044b \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0442\u044c \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u043e\u0435 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u0432 \u043d\u043e\u0432\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u2014 \u043e\u0442 \u0440\u0435\u0430\u043b\u0438\u0441\u0442\u0438\u0447\u043d\u043e\u0439 \u0444\u043e\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0438 \u0434\u043e \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0430\u043d\u0442\u0430\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0446\u0435\u043d\u044b.\u0420\u0438\u0441\u0443\u043d\u043e\u043a 2. \u041f\u0440\u0438\u043c\u0435\u0440 \u0433\u0435\u043d\u0435\u0440\u0430\u0446\u0438\u0438 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0439 \u0432 Stable Diffusion 3.5\u041d\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 Flow Matching\u2019\u0430 \u043d\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0438\u0432\u0430\u0435\u0442\u0441\u044f. \u0421 \u0435\u0433\u043e \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u043e\u0436\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0438 \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0435 \u043e\u0431\u044a\u0435\u043a\u0442\u044b \u2014 \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440,\u00a0\u0432\u0438\u0434\u0435\u043e \u0432\u043c\u0435\u0441\u0442\u0435 \u0441\u043e \u0437\u0432\u0443\u043a\u043e\u043c. 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