Learning few-step posterior samplers by unfolding and distillation of diffusion models

Diffusion models (DMs) have emerged as powerful image priors in Bayesian computational imaging. Two primary strategies have been proposed for leveraging DMs in this context: Plug-and-Play methods, which are zero-shot and highly flexible but rely on approximations; and specialized conditional DMs, which achieve higher accuracy and faster inference for specific tasks through supervised training. In this work, we introduce a novel framework that integrates deep unfolding and model distillation to transform a DM image prior into a few-step conditional model for posterior sampling. A central innovation of our approach is the unfolding of a Markov chain Monte Carlo (MCMC) algorithm - specifically, the recently proposed LATINO Langevin sampler (Spagnoletti et al., 2025) - representing the first known instance of deep unfolding applied to a Monte Carlo sampling scheme. We demonstrate our proposed unfolded and distilled samplers through extensive experiments and comparisons with the state of the art, where they achieve excellent accuracy and computational efficiency, while retaining the flexibility to adapt to variations in the forward model at inference time.