[2603.03700] Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data

Statistics > Machine Learning arXiv:2603.03700 (stat) [Submitted on 4 Mar 2026] Title:Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data Authors:Saptarshi Chakraborty, Quentin Berthet, Peter L. Bartlett View a PDF of the paper titled Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data, by Saptarshi Chakraborty and 2 other authors View PDF HTML (experimental) Abstract:Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional structure common in real data, such as that arising in natural images. In this work, we study the statistical convergence of score-based diffusion models for learning an unknown distribution $\mu$ from finitely many samples. Under mild regularity conditions on the forward diffusion process and the data distribution, we derive finite-sample error bounds on the learned generative distribution, measured in the Wasserstein-$p$ distance. Unlike prior results, our guarantees hold for all $p \ge 1$ and require only a finite-moment assumption on $\mu$, without compact-support, manifold, or smooth-density conditions. Specifically, given $n$ i.i.d.\ samples from $\mu$ with finite $q$-th moment and appropriately chosen network architectures, hyperparameters, and discretization schemes, we sho...