Conditional Mutual Information Based Diffusion Posterior Sampling for Solving Inverse Problems

TL;DR

This paper introduces an information-theoretic method using conditional mutual information to improve diffusion model-based solutions for inverse problems, leading to better image reconstruction quality.

Contribution

It proposes maximizing conditional mutual information to enhance diffusion models' effectiveness in solving inverse problems without additional training.

Findings

Improved image quality in inverse problem solutions

Seamless integration with existing diffusion approaches

Quantitative performance gains demonstrated

Abstract

Inverse problems are prevalent across various disciplines in science and engineering. In the field of computer vision, tasks such as inpainting, deblurring, and super-resolution are commonly formulated as inverse problems. Recently, diffusion models (DMs) have emerged as a promising approach for addressing noisy linear inverse problems, offering effective solutions without requiring additional task-specific training. Specifically, with the prior provided by DMs, one can sample from the posterior by finding the likelihood. Since the likelihood is intractable, it is often approximated in the literature. However, this approximation compromises the quality of the generated images. To overcome this limitation and improve the effectiveness of DMs in solving inverse problems, we propose an information-theoretic approach. Specifically, we maximize the conditional mutual information $\mathrm{I}(\boldsymbol{x}_0; \boldsymbol{y} | \boldsymbol{x}_t)$, where $\boldsymbol{x}_0$ represents the reconstructed signal, $\boldsymbol{y}$ is the measurement, and $\boldsymbol{x}_t$ is the intermediate signal at stage $t$. This ensures that the intermediate signals $\boldsymbol{x}_t$ are generated in a way that the final reconstructed signal $\boldsymbol{x}_0$ retains as much information as possible about the measurement $\boldsymbol{y}$. We demonstrate that this method can be seamlessly integrated with recent approaches and, once incorporated, enhances their performance both qualitatively and quantitatively.