Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution

TL;DR

This paper introduces a fast diffusion EM algorithm that jointly estimates images and unknown degradation parameters, like blur kernels, in blind inverse problems, improving efficiency and effectiveness in deblurring tasks.

Contribution

The paper proposes a novel EM-based approach combining diffusion models and a new blur kernel regularization, enabling joint estimation of images and unknown parameters efficiently.

Findings

Outperforms state-of-the-art blind deblurring methods

Provides a faster version of the diffusion EM algorithm

Demonstrates strong results on blind image deblurring tasks

Abstract

Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the efficiency of those models to jointly estimate the restored image and unknown parameters of the degradation model such as blur kernel. In particular, we designed an algorithm based on the well-known Expectation-Minimization (EM) estimation method and diffusion models. Our method alternates between approximating the expected log-likelihood of the inverse problem using samples drawn from a diffusion model and a maximization step to estimate unknown model parameters. For the maximization step, we also introduce a novel blur kernel regularization based on a Plug \& Play denoiser. Diffusion models are long to run, thus we provide a fast version of our algorithm. Extensive experiments on blind image deblurring demonstrate the effectiveness of our method when compared to other state-of-the-art approaches.