Year: 2025
Type: preprint
Abstract: 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 $\beta$-smooth H\"older 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 $n^{-(\beta+1)/(2\beta+d)}$ up to polylogarithmic factors. Our unified analysis handles arbitrary smoothness $\beta > 0$, 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.
Source: arXiv (Cornell University)
Institutions: Centre National de la Recherche Scientifique, Université Paris Cité, Sorbonne Université, Département de mathématiques et applications, Laboratoire de Probabilités, Statistique et Modélisation, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Institut de recherche mathématique de Rennes
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415099823