Reverse Diffusion Sequential Monte Carlo Samplers

2025-08-07

AI Summary

Existing diffusion samplers suffer from accumulating bias due to time discretization and errors in score estimation, degrading sample quality and impairing unbiased estimation of the normalization constant. To address this, we propose a Sequential Monte Carlo (SMC) method grounded in the inverse denoising diffusion process. Our approach is the first to explicitly model diffusion samplers as proposal distributions within SMC and systematically correct bias by progressively constructing intermediate target distributions. Crucially, the method requires no additional training and yields an unbiased estimator of the normalization constant under the SMC framework. Empirical evaluation on synthetic distributions and real-world Bayesian inference tasks demonstrates substantial improvements in sampling stability and estimator consistency. This work establishes a new paradigm for exact probabilistic inference with diffusion models.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• 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

We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using approximate score functions, they can suffer from accumulating errors due to time discretization and imperfect score estimation. In this work, we introduce a principled SMC framework that formalizes diffusion-based samplers as proposals while systematically correcting for their biases. The core idea is to construct informative intermediate target distributions that progressively steer the sampling trajectory toward the final target distribution. Although ideal intermediate targets are intractable, we develop exact approximations using quantities from the score estimation-based proposal, without requiring additional model training or inference overhead. The resulting sampler, termed RDSMC, enables consistent sampling and unbiased estimation of the target's normalization constant under mild conditions. We demonstrate the effectiveness of our method on a range of synthetic targets and real-world Bayesian inference problems.

Problem

• Sampling from unnormalized target distributions using reverse diffusion
• Correcting biases in diffusion-based samplers with SMC framework
• Enabling consistent sampling and unbiased normalization constant estimation

Innovation

• Reverse diffusion SMC for unnormalized sampling
• Exact approximations without extra training overhead
• Consistent sampling with unbiased normalization estimation