{"id":1618,"date":"2025-02-03T07:02:56","date_gmt":"2025-02-03T07:02:56","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/02\/03\/2501-18863\/"},"modified":"2025-02-03T07:02:56","modified_gmt":"2025-02-03T07:02:56","slug":"2501-18863","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/02\/03\/2501-18863\/","title":{"rendered":"Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models"},"content":{"rendered":"

Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models
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arXiv:2501.18863v1 Announce Type: new
\nAbstract: Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability flow ODE, a widely used diffusion-based sampler known for its practical efficiency. While a number of prior works address its general convergence theory, it remains unclear whether the probability flow ODE sampler can adapt to the low-dimensional structures commonly present in natural image data. We demonstrate that, with accurate score function estimation, the probability flow ODE sampler achieves a convergence rate of $O(k\/T)$ in total variation distance (ignoring logarithmic factors), where $k$ is the intrinsic dimension of the target distribution and $T$ is the number of iterations. This dimension-free convergence rate improves upon existing results that scale with the typically much larger ambient dimension, highlighting the ability of the probability flow ODE sampler to exploit intrinsic low-dimensional structures in the target distribution for faster sampling.<\/div>\n

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\n Jiaqi Tang, Yuling Yan
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Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models arXiv:2501.18863v1 Announce Type: new Abstract: Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability flow ODE, a widely used diffusion-based […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[1274,1612,921],"class_list":["post-1618","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-convergence","tag-flow","tag-probability"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1618"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=1618"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1618\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=1618"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=1618"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=1618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}