Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach

2025/06/04 by Haoxuan Chen, Chen, Haoxuan, Yinuo Ren +7 · 6 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Generative Adversarial Networks and Image Synthesis #Image and Video Processing (eess.IV) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2506.03979

openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior sampling methods proposed for solving common BIPs rely on heuristic approximations to the generative process. To exploit the generative capability of DMs and avoid the usage of such approximations, we propose an ensemble-based algorithm that performs posterior sampling without the use of heuristic approximations. Our algorithm is motivated by existing works that combine DM-based methods with the sequential Monte Carlo (SMC) method. By examining how the prior evolves through the diffusion process encoded by the pre-trained score function, we derive a modified partial differential equation (PDE) governing the evolution of the corresponding posterior distribution. This PDE includes a modified diffusion term and a reweighting term, which can be simulated via stochastic weighted particle methods. Theoretically, we prove that the error between the true posterior distribution can be bounded in terms of the training error of the pre-trained score function and the number of particles in the ensemble. Empirically, we validate our algorithm on several inverse problems in imaging to show that our method gives more accurate reconstructions compared to existing DM-based methods.

Cited by

• Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimization
• SAIP: A Plug-and-Play Scale-adaptive Module in Diffusion-based Inverse Problems
• TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion
• DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models
• A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
• MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control

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