Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization

ArXi:2401.15604v4 Announce Type: replace Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on algorithm-agnostic assumptions and treats empirical risk minimization as if it were solved exactly. In practice, however, score functions are parameterized by highly nonconvex neural networks and trained by gradient descent (GD), and it remains unclear whether such practical procedures admit rigorous guarantees.