Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems

This work presents a unified analysis of variance reduction techniques for sampling from high-dimensional, non-log-concave distributions, addressing challenges in scenarios where exact gradients are unavailable. The authors establish improved non-asymptotic convergence rates in terms of Fisher information and total variation distance, and demonstrate the applicability of these techniques in solving inverse problems with score-based generative priors. The empirical results show that variance reduction methods enhance sample quality in imaging tasks, which is significant for practitioners dealing with complex sampling scenarios in machine learning.