Diffusion Score Estimation with Shallow Neural Networks: Regularity, Approximation, and Finite-Sample Rates
We study the sample complexity of estimating Ornstein--Uhlenbeck diffusion scores in $\mathbb R^d$ using denoising score matching (DSM) with finite-width shallow ReLU networks, and its implications for reverse-process sampling. Under weak differentiability and polynomial-growth conditions on normalized derivatives of the initial density, we combine complementary estimates from the Gaussian transition kernel and the initial density to obtain explicit Sobolev bounds that are uniform in time on each fixed ball. Combining these bounds with existing shallow-network approximation theory gives explicit control of the approximation error and a sufficient path-norm budget. We then use truncation a...
| Authors | Fan Liu, Yahong Yang, Wei Zhu |
|---|---|
| Primary category | stat.ML |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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