Improving Diffusion Models for Inverse Problems using Manifold Constraints

TL;DR

This paper introduces a manifold constraint correction for diffusion model-based inverse problem solvers, significantly improving their accuracy by keeping samples on the data manifold, demonstrated across various image restoration tasks.

Contribution

The paper proposes a simple yet effective manifold constraint correction to enhance diffusion-based inverse problem solvers, leading to substantial performance improvements.

Findings

Improved results in image inpainting, colorization, and CT reconstruction.

The correction method is easy to implement and boosts performance.

The approach is supported by both theoretical analysis and extensive experiments.

Abstract

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion