Improving Decoupled Posterior Sampling for Inverse Problems using Data Consistency Constraint

TL;DR

This paper introduces Guided Decoupled Posterior Sampling (GDPS), a novel method that incorporates data consistency constraints into diffusion-based inverse problem solving, leading to improved accuracy and convergence.

Contribution

The paper proposes GDPS, integrating data consistency into decoupled posterior sampling, enhancing inverse problem solutions and extending scalability to latent diffusion models.

Findings

GDPS outperforms existing methods on FFHQ and ImageNet datasets.

GDPS achieves state-of-the-art accuracy in various inverse tasks.

The method improves convergence and robustness under challenging conditions.

Abstract

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been recently proposed. However, the reverse process in these methods ignores measurement information, leading to errors that impede effective optimization in subsequent steps. To solve this problem, we propose Guided Decoupled Posterior Sampling (GDPS) by integrating a data consistency constraint in the reverse process. The constraint performs a smoother transition within the optimization process, facilitating a more effective convergence toward the target distribution. Furthermore, we extend our method to latent diffusion models and Tweedie's formula, demonstrating its scalability. We evaluate GDPS on the FFHQ and ImageNet datasets across various linear and nonlinear tasks under both standard and challenging conditions. Experimental results demonstrate that GDPS achieves state-of-the-art performance, improving accuracy over existing methods.