Improving Diffusion Posterior Samplers with Lagged Temporal Corrections for Image Restoration

TL;DR

This paper introduces LAMP, a novel diffusion posterior sampler that incorporates lagged temporal corrections for improved image restoration, achieving better results without additional denoising steps.

Contribution

LAMP extends diffusion posterior sampling with second-order discretization and lagged corrections, providing a modular plug-in that enhances performance in inverse imaging problems.

Findings

LAMP outperforms strong baselines like DiffPIR and DDRM.

LAMP improves image restoration quality without increasing denoising evaluations.

The method offers a bias-variance trade-off analysis for better transition modeling.

Abstract

Diffusion-based posterior sampling (PS) is a leading framework for imaging inverse problems, combining learned priors with measurement constraints. Yet, its standard formulations rely on instantaneous data-consistent estimates, which induce temporal variability in the reverse dynamics. We reinterpret PS from a dynamical perspective, showing that the standard PS update corresponds to a first-order discretization of the diffusion dynamics plus a residual correction capturing the mismatch between the denoised prediction and the data-consistent estimate. A second-order discretization, however, naturally introduces a temporal correction based on the variation of consecutive estimates. Building on this, we propose LAMP, combining the second-order update with the residual correction characterizing a PS technique. LAMP thus inherits a lagged temporal correction, and it can be implemented as a modular plug-in over the PS backbone. We show that LAMP preserves the structure of a posterior sampler, and we perform a one-step risk analysis to characterize when LAMP improves the reverse transition via a bias-variance trade-off. Experiments across multiple imaging tasks demonstrate consistent improvements over strong baselines such as DiffPIR and DDRM, without increasing the number of denoising evaluations.