Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing

TL;DR

This paper introduces DAPS, a novel noise annealing method for diffusion models that enhances inverse problem solving by decoupling sampling steps, leading to better exploration and improved reconstruction quality.

Contribution

The paper proposes Decoupled Annealing Posterior Sampling (DAPS), a new approach that decouples diffusion steps to improve inverse problem solutions in nonlinear scenarios.

Findings

DAPS improves sample quality in image restoration tasks.

DAPS increases success rates in nonlinear inverse problems.

DAPS enhances stability of diffusion-based inverse problem solving.

Abstract

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to correct errors from earlier sampling steps, leading to worse performance in complicated nonlinear inverse problems, such as phase retrieval. To address this challenge, we propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems.