Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
This work addresses the need for precise performance assessment of diffusion models in inverse problems for researchers, though it is incremental as it focuses on a constrained Gaussian case.
The paper tackled the problem of evaluating the accuracy of diffusion models as priors for inverse problems like deblurring, specifically for Gaussian data distributions, by computing the exact Wasserstein distance between the diffusion model's output and the ideal solution distribution, enabling comparison of different algorithms.
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.