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 normali