Abstract

Diffusion models have become indispensable tools for data generation and synthesis in domains as diverse as computer vision, natural language processing, and molecule generation. A key requirement for their usefulness is the fidelity of the generated samples to the underlying data distribution. Reflected generative diffusion models, which rely on the reversion of reflected SDEs, offer a promising way to accurately capture the complexity of real-world data distributions. We focus on the statistical question of how effectively these models implicitly learn the true data distribution by learning the empirical score, exploring both the approximation and generalization capabilities of this approach, and we provide an explicit upper bound on the estimation error of the generated data distribution. Our results show that nearly minimax optimal convergence rate under Besov smoothness assumptions for the estimation error in the total variation distance can be attained.