Bayesian computation with generative diffusion models by Multilevel Monte Carlo

TL;DR

This paper introduces a Multilevel Monte Carlo method that leverages diffusion models for Bayesian inverse problems, significantly reducing computational costs while maintaining accuracy in large-scale imaging applications.

Contribution

It proposes a novel multilevel Monte Carlo approach that couples diffusion models of varying accuracy to lower computational costs in Bayesian sampling.

Findings

Achieves 4x to 8x cost reduction compared to standard methods.

Maintains high accuracy in Bayesian posterior sampling.

Effective in large-scale computational imaging problems.

Abstract

Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion models often require a large number of neural function evaluations per sample in order to deliver accurate posterior samples. As a result, using diffusion models as stochastic samplers for Monte Carlo integration in Bayesian computation can be highly computationally expensive, particularly in applications that require a substantial number of Monte Carlo samples for conducting uncertainty quantification analyses. This cost is especially high in large-scale inverse problems such as computational imaging, which rely on large neural networks that are expensive to evaluate. With quantitative imaging applications in mind, this paper presents a Multilevel Monte Carlo strategy that significantly reduces the cost of Bayesian computation with diffusion models. This is achieved by exploiting cost-accuracy trade-offs inherent to diffusion models to carefully couple models of different levels of accuracy in a manner that significantly reduces the overall cost of the calculation, without reducing the final accuracy. The proposed approach achieves a $4\times$-to-$8\times$ reduction in computational cost w.r.t. standard techniques across three benchmark imaging problems.