AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-20
Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
Diffusion models are widely used to represent complex priors in Bayesian inverse problems, but existing posterior sampling methods rely on heuristic approximations to the generative process. The authors propose an ensemble-based algorithm, motivated by combining diffusion models with sequential Monte Carlo, that performs posterior sampling without heuristic approximations. They prove that the error between the true posterior and the generated samples' empirical distribution can be bounded by the pre-trained score function's training error and the number of particles, and on several imaging inverse problems the method gives more accurate reconstructions than existing diffusion-model-based methods.