DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models

TL;DR

DMPlug introduces a novel plug-in approach utilizing pretrained diffusion models to effectively solve inverse problems, addressing manifold and measurement feasibility, and demonstrating robustness to noise across various linear and nonlinear tasks.

Contribution

The paper proposes DMPlug, a new plug-in method that leverages pretrained diffusion models to improve inverse problem solving, especially for nonlinear and noisy scenarios.

Findings

DMPlug outperforms state-of-the-art methods on multiple inverse problem tasks.

It demonstrates robustness to unknown noise types and levels.

The method is effective for both linear and nonlinear inverse problems.

Abstract

Pretrained diffusion models (DMs) have recently been popularly used in solving inverse problems (IPs). The existing methods mostly interleave iterative steps in the reverse diffusion process and iterative steps to bring the iterates closer to satisfying the measurement constraint. However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility) and fit the measurement (i.e., measurement feasibility), especially for nonlinear IPs. Moreover, their capabilities to deal with noisy IPs with unknown types and levels of measurement noise are unknown. In this paper, we advocate viewing the reverse process in DMs as a function and propose a novel plug-in method for solving IPs using pretrained DMs, dubbed DMPlug. DMPlug addresses the issues of manifold feasibility and measurement feasibility in a principled manner, and also shows great potential for being robust to unknown types and levels of noise. Through extensive experiments across various IP tasks, including two linear and three nonlinear IPs, we demonstrate that DMPlug consistently outperforms state-of-the-art methods, often by large margins especially for nonlinear IPs. The code is available at https://github.com/sun-umn/DMPlug.