Dual Ascent Diffusion for Inverse Problems

TL;DR

This paper introduces a dual ascent optimization framework for inverse problems using diffusion model priors, improving image quality, robustness, and speed over existing methods.

Contribution

It presents a novel dual ascent approach for MAP problems with diffusion priors, enhancing accuracy and efficiency in inverse problem solutions.

Findings

Achieves better image quality in restoration tasks

More robust to high measurement noise

Faster and more faithful solutions than current methods

Abstract

Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior sampling approaches, however, rely on different computational approximations, leading to inaccurate or suboptimal samples. To address this issue, we introduce a new approach to solving MAP problems with diffusion model priors using a dual ascent optimization framework. Our framework achieves better image quality as measured by various metrics for image restoration problems, it is more robust to high levels of measurement noise, it is faster, and it estimates solutions that represent the observations more faithfully than the state of the art.