# Picard Proximal Monte Carlo for Parallel Bayesian Imaging with Score-Based Generative Priors

arXiv: https://arxiv.org/abs/2608.17666 · HTML: https://mlsanity.com/paper/2608.17666/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 99 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetry](https://mlsanity.com/paper/1911.01469/) (2019)
- [Convergence of the Inexact Langevin Algorithm in KL Divergence with Application to Score-based Generative Models](https://mlsanity.com/paper/2211.01512/) (2022)
- [Fast and Efficient Parallel Sampling Using Higher Order Langevin Dynamics](https://mlsanity.com/paper/2510.18242/) (2025)

## Abstract (arXiv)

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 512×512×80 sparse-view computed tomography (CT) problem, annealed multi-block PiX-MC achieves up to a 50× runtime speedup over the standard Langevin sampler using eight GPUs.