Score-Based Metropolis-Hastings Algorithms

TL;DR

This paper presents a novel method that combines score-based models with Metropolis-Hastings algorithms by estimating acceptance probabilities, enabling more accurate and flexible sampling, especially for complex distributions.

Contribution

The paper introduces a new loss function based on detailed balance, allowing score-based models to incorporate Metropolis-Hastings acceptance criteria.

Findings

Effective sampling from heavy-tail distributions.

Enables Metropolis-Hastings adjustments with score-based models.

Improves sampling accuracy over traditional Langevin methods.

Abstract

In this paper, we introduce a new approach for integrating score-based models with the Metropolis-Hastings algorithm. While traditional score-based diffusion models excel in accurately learning the score function from data points, they lack an energy function, making the Metropolis-Hastings adjustment step inaccessible. Consequently, the unadjusted Langevin algorithm is often used for sampling using estimated score functions. The lack of an energy function then prevents the application of the Metropolis-adjusted Langevin algorithm and other Metropolis-Hastings methods, limiting the wealth of other algorithms developed that use acceptance functions. We address this limitation by introducing a new loss function based on the \emph{detailed balance condition}, allowing the estimation of the Metropolis-Hastings acceptance probabilities given a learned score function. We demonstrate the effectiveness of the proposed method for various scenarios, including sampling from heavy-tail distributions.