MCMC-Correction of Score-Based Diffusion Models for Model Composition

TL;DR

This paper introduces a novel Metropolis-Hastings-like acceptance rule for score-based diffusion models, enabling MCMC sampling and model composition without explicit energy functions.

Contribution

It proposes a new acceptance rule based on score line integration, allowing MCMC techniques with existing score-based models.

Findings

Improved sampling quality comparable to energy-based models.

Enables model composition using pre-trained score-based diffusion models.

Applicable to synthetic and real-world data.

Abstract

Diffusion models can be parameterized in terms of either score or energy function. The energy parameterization is attractive as it enables sampling procedures such as Markov Chain Monte Carlo (MCMC) that incorporates a Metropolis--Hastings (MH) correction step based on energy differences between proposed samples. Such corrections can significantly improve sampling quality, particularly in the context of model composition, where pre-trained models are combined to generate samples from novel distributions. Score-based diffusion models, on the other hand, are more widely adopted and come with a rich ecosystem of pre-trained models. However, they do not, in general, define an underlying energy function, making MH-based sampling inapplicable. In this work, we address this limitation by retaining score parameterization and introducing a novel MH-like acceptance rule based on line integration of the score function. This allows the reuse of existing diffusion models while still combining the reverse process with various MCMC techniques, viewed as an instance of annealed MCMC. Through experiments on synthetic and real-world data, we show that our MH-like samplers {yield relative improvements of similar magnitude to those observed} with energy-based models, without requiring explicit energy parameterization.