{"ID":2897436,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.04794","arxiv_id":"2507.04794","title":"Generalization bounds for score-based generative models: a synthetic proof","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 $β$-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 $β\u003e 0$, 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.","short_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 $β$-smooth Hölder class with either compact support or subGaussian tails on $\\mathbb{R}^d$, we prove that neural network-based score estimator...","url_abs":"https://arxiv.org/abs/2507.04794","url_pdf":"https://arxiv.org/pdf/2507.04794v1","authors":"[\"Arthur Stéphanovitch\",\"Eddie Aamari\",\"Clément Levrard\"]","published":"2025-07-07T09:13:09Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[\"Diffusion Model\"]","has_code":false}