PiX-MC Accelerates Parallel Bayesian Imaging with Generative Priors.

Bayesian imaging inverse problems often demand sampling from extremely high-dimensional posterior distributions, a computationally intensive task. While modern score-based and diffusion models offer powerful Bayesian priors, their sequential sampling procedures remain a bottleneck for large-scale imaging applications. This paper presents PiX-MC (Picard Proximal Monte Carlo), a novel time-parallel posterior sampling framework designed to overcome these limitations. PiX-MC combines proximal Langevin dynamics with Picard iteration, exploiting the efficiency of problem-specific proximal operators for many imaging likelihoods. The Picard refinement inherently exposes parallelism across discretization nodes, making it naturally suitable for multi-GPU implementations. To further enhance scalability and sampling performance, the authors developed multi-block and annealed variants of the framework. Rigorous convergence guarantees are established, even for non-log-concave posteriors, imperfect learned score models, and multi-block/annealing strategies. Experimental results across diverse imaging inverse problems demonstrate that PiX-MC substantially reduces wall-clock time while maintaining high reconstruction quality, achieving up to a 50x speedup over standard Langevin samplers on a complex CT problem using eight GPUs.