Improving Diffusion Posterior Samplers with Lagged Temporal Corrections for Image Restoration

2026-05-12

AI Summary

This work addresses the temporal instability in existing diffusion posterior sampling methods, which stems from reliance on instantaneous data consistency estimates. From a dynamical systems perspective, we propose LAMP—a novel approach that incorporates a lagged time-correction mechanism via second-order discretization and integrates a residual refinement term to enhance sample quality. LAMP is the first method to combine lagged correction with posterior sampling, functioning as a plug-and-play module that improves the bias-variance trade-off without requiring additional denoising calls. Experimental results demonstrate that LAMP consistently outperforms strong baselines such as DiffPIR and DDRM across a range of image restoration tasks.

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.

Problem

• diffusion posterior sampling
• image restoration
• temporal variability
• inverse problems
• data consistency

Innovation

• diffusion posterior sampling
• temporal correction
• second-order discretization
• image restoration
• LAMP