Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey

2025-10-15

AI Summary

This work addresses Bayesian inverse problems using pre-trained diffusion models—without fine-tuning or additional training. The core method introduces a *distribution warping* mechanism that explicitly modifies the prior distribution at intermediate diffusion steps to align with observed data, thereby transforming posterior sampling into Monte Carlo sampling (e.g., importance sampling or MCMC) over the warped latent distribution. This framework unifies diverse sampling strategies as systematic corrections to the implicit latent variable distributions along the diffusion trajectory. Experiments demonstrate high accuracy and strong generalization across image reconstruction and scientific computing tasks, significantly enhancing the plug-and-play applicability of pre-trained diffusion models for Bayesian inference.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Bayesian Learning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage emph{pre-trained} diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a emph{twisting} mechanism for the intermediate distributions within the diffusion process, guiding the simulations toward the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.

Problem

• Leveraging pre-trained diffusion models for Bayesian inverse problems
• Employing twisting mechanisms to guide posterior distribution sampling
• Integrating Monte Carlo methods with diffusion processes without retraining

Innovation

• Leveraging pre-trained diffusion models as priors
• Using twisting mechanisms for intermediate distributions
• Applying Monte Carlo methods for posterior sampling