保存先:
| 主要な著者: | , |
|---|---|
| フォーマット: | Preprint |
| 出版事項: |
2024
|
| 主題: | |
| オンライン･アクセス: | https://arxiv.org/abs/2402.08082 |
| タグ: |
タグ追加
タグなし, このレコードへの初めてのタグを付けませんか!
|
目次:
- While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.