Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz Estimates Article Swipe
Connor Mooney
,
Zhongjian Wang
,
Jack Xin
,
Yu Yifeng
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2405.16104
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2405.16104
We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function with optimal time length. The optimality is validated by an example whose Lipschitz constant of scores is bounded at initial but blows up in finite time. This necessitates the separation of time scales in conventional bounds for non-log-concave distributions. In contrast, our follow up analysis only relies on a local Lipschitz condition and is valid globally in time. This leads to the convergence of numerical scheme without time separation. For the non-smooth case, we show that the optimal Lipschitz bound is O(1/t) in the point-wise sense for distributions supported on a compact, smooth and low-dimensional manifold with boundary.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2405.16104
- https://arxiv.org/pdf/2405.16104
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4399115258
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https://openalex.org/W4399115258Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2405.16104Digital Object Identifier
- Title
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Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz EstimatesWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-05-25Full publication date if available
- Authors
-
Connor Mooney, Zhongjian Wang, Jack Xin, Yu YifengList of authors in order
- Landing page
-
https://arxiv.org/abs/2405.16104Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2405.16104Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2405.16104Direct OA link when available
- Concepts
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Lipschitz continuity, Convergence (economics), Mathematics, Applied mathematics, Generative grammar, Econometrics, Mathematical analysis, Computer science, Economics, Artificial intelligence, MacroeconomicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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