Diffusion Model Based Sampling with Metropolis-Hastings Correction

Abstract

This thesis investigates unbiased sampling from complex and higher dimensional prob-ability distributions using score-based diffusion models. While diffusion samplers have demonstrated strong generative performance, they inherently produce biased samples due to discretization errors and imperfect score estimation. To address this limitation, we de- velop a Metropolis–Hastings corrected diffusion framework that preserves the flexibility of diffusion-based proposals while guaranteeing asymptotic exactness. By deriving closed- form forward and reverse diffusion kernels, our method enables valid acceptance–rejection steps without approximations. Numerical experiments on multimodal synthetic targets demonstrate that our approach reduces sampling bias and improves posterior accuracy, while maintaining efficient mixing compared to traditional Markov chain methods. This work contributes to the fields of Bayesian statistics and machine learning by bridging deep generative diffusion models with theoretically rigorous MCMC, offering a practical tool for exact inference in challenging high-dimensional settings.