Reflected diffusions provide a principled way to build adaptive importance samplers for bounded-domain integration without requiring boundary corrections, and can handle non-smooth integrands using gradient-free training.
This paper develops a method for estimating integrals over bounded regions in high dimensions by combining learned diffusion models with reflected dynamics. Instead of standard sampling approaches, the method trains a neural network to reverse a diffusion process that stays within the domain boundary, enabling importance sampling that adapts to where the integrand is concentrated.