Solving Inverse Problems using Diffusion with Iterative Colored Renoising

TL;DR

This paper introduces DDfire, a novel iterative reestimation method that enhances diffusion models for solving inverse imaging problems, achieving state-of-the-art accuracy and efficiency.

Contribution

The paper proposes FIRE, an iterative reestimation and renoising technique that improves gradient approximation in diffusion-based inverse problem solving, integrated into DDIM as DDfire.

Findings

DDfire outperforms existing methods in accuracy.

DDfire achieves faster runtimes.

Effective on multiple inverse imaging tasks.

Abstract

Imaging inverse problems can be solved in an unsupervised manner using pre-trained diffusion models, but doing so requires approximating the gradient of the measurement-conditional score function in the diffusion reverse process. We show that the approximations produced by existing methods are relatively poor, especially early in the reverse process, and so we propose a new approach that iteratively reestimates and "renoises" the estimate several times per diffusion step. This iterative approach, which we call Fast Iterative REnoising (FIRE), injects colored noise that is shaped to ensure that the pre-trained diffusion model always sees white noise, in accordance with how it was trained. We then embed FIRE into the DDIM reverse process and show that the resulting "DDfire" offers state-of-the-art accuracy and runtime on several linear inverse problems, as well as phase retrieval. Our implementation is at https://github.com/matt-bendel/DDfire