Picard Proximal Monte Carlo for Parallel Bayesian Imaging with Score-Based Generative Priors
Deliang WeiEvan BellWenhan GuoYifan ChenYu Sun
Aug 2026
Machine Learning
Abstract
Bayesian imaging inverse problems often require sampling from high-dimensional posterior distributions. While recent score-based and diffusion models provide expressive Bayesian priors, their sampling procedures remain inherently sequential and computationally expensive for large-scale imaging applications. We propose PiX-MC, a time-parallel posterior sampling framework based on proximal Langevin dynamics and Picard iteration. The proximal-likelihood formulation exploits the fact that many imaging likelihoods admit efficient, problem-specific proximal operators, while Picard refinement exposes parallelism across discretization nodes and naturally supports multi-GPU implementation. To further improve practical scalability and sampling performance, we develop multi-block and annealed variants of the proposed framework. We establish convergence guarantees under transparent assumptions, accommodating non-log-concave posteriors, imperfect learned score models, multi-block implementations, and annealing schedules. Experiments on a diverse collection of imaging inverse problems demonstrate that PiX-MC substantially reduces wall-clock time while preserving reconstruction quality. On a $512\times512\times80$ sparse-view computed tomography (CT) problem, annealed multi-block PiX-MC achieves up to a $50\times$ runtime speedup over the standard Langevin sampler using eight GPUs.
This article investigates several physics-informed and hybrid machine learning strategies that incorporate physics knowledge in experimental data-driven deep-learning models for predicting the bond quality and porosity of fused filament fabrication (FFF) parts. Three types of strategies are explored to incorporate physics constraints and multi-physics FFF simulation results into a deep neural network (DNN), thus ensuring consistency with physical laws: (1) incorporate physics constraints within the loss function of the DNN, (2) use physics model outputs as additional inputs to the DNN model, and (3) pre-train a DNN model with physics model input-output and then update it with experimental data. These strategies help to enforce a physically consistent relationship between bond quality and tensile strength, thus making porosity predictions physically meaningful. Eight different combinations of the above strategies are investigated. The results show how the combination of multiple strategies produces accurate machine learning models even with limited experimental data.
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