Generalization bounds for score-based generative models: a synthetic proof
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909677352124416 |
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| author | Stéphanovitch, Arthur Aamari, Eddie Levrard, Clément |
| author_facet | Stéphanovitch, Arthur Aamari, Eddie Levrard, Clément |
| contents | We establish minimax convergence rates for score-based generative models (SGMs) under the $1$-Wasserstein distance. Assuming the target density $p^\star$ lies in a nonparametric $β$-smooth Hölder class with either compact support or subGaussian tails on $\mathbb{R}^d$, we prove that neural network-based score estimators trained via denoising score matching yield generative models achieving rate $n^{-(β+1)/(2β+d)}$ up to polylogarithmic factors. Our unified analysis handles arbitrary smoothness $β> 0$, supports both deterministic and stochastic samplers, and leverages shape constraints on $p^\star$ to induce regularity of the score. The resulting proofs are more concise, and grounded in generic stability of diffusions and standard approximation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalization bounds for score-based generative models: a synthetic proof Stéphanovitch, Arthur Aamari, Eddie Levrard, Clément Statistics Theory We establish minimax convergence rates for score-based generative models (SGMs) under the $1$-Wasserstein distance. Assuming the target density $p^\star$ lies in a nonparametric $β$-smooth Hölder class with either compact support or subGaussian tails on $\mathbb{R}^d$, we prove that neural network-based score estimators trained via denoising score matching yield generative models achieving rate $n^{-(β+1)/(2β+d)}$ up to polylogarithmic factors. Our unified analysis handles arbitrary smoothness $β> 0$, supports both deterministic and stochastic samplers, and leverages shape constraints on $p^\star$ to induce regularity of the score. The resulting proofs are more concise, and grounded in generic stability of diffusions and standard approximation theory. |
| title | Generalization bounds for score-based generative models: a synthetic proof |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2507.04794 |