Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions

TL;DR

This paper provides an exact analysis of the accuracy of diffusion models in solving inverse problems with Gaussian data, focusing on deblurring, by computing the Wasserstein distance between model outputs and ideal solutions.

Contribution

It introduces a precise method to evaluate diffusion model accuracy for Gaussian inverse problems by calculating the exact Wasserstein distance, enabling direct comparison of algorithms.

Findings

Exact Wasserstein distance computation for diffusion models and Gaussian inverse problems

Quantitative comparison of different diffusion-based algorithms

Insights into the discrepancy between theoretical and practical solutions

Abstract

Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as inpainting, super-resolution, and deblurring. However, several unresolved questions remain about how well they perform. In this article, we investigate the accuracy of these models when applied to a Gaussian data distribution for deblurring. Within this constrained context, we are able to precisely analyze the discrepancy between the theoretical resolution of inverse problems and their resolution obtained using diffusion models by computing the exact Wasserstein distance between the distribution of the diffusion model sampler and the ideal distribution of solutions to the inverse problem. Our findings allow for the comparison of different algorithms from the literature.