Abstract

Diffusion-based generative models have recently attracted significant interest in statistics and machine learning, yet their theoretical properties remain only partially understood. We study a non-standard class of denoising reflected diffusion models that address limitations of conventional designs in unbounded domains by introducing a reflected noise process. For these models, we establish minimax optimal convergence rates in total variation up to polylogarithmic factors under Sobolev smoothness. Our analysis is based on a refined spatio-temporal approximation of the score function via spectral methods and a rigorous treatment of neural network estimation. The results yield a precise characterisation of the statistical complexity of this model class and provide insight into the interplay between geometry, regularity, and learnability. Based on joint work with Sören Christensen, Asbjørn Holk, and Lukas Trottner.