Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers

TL;DR

This paper introduces Measurement-Consistent Langevin Corrector (MCLC), a stabilization module for latent diffusion model-based inverse problem solvers that improves stability by aligning solver dynamics with learned reverse diffusion dynamics.

Contribution

The paper proposes MCLC, a theoretically grounded, plug-and-play stabilization method that enhances the stability and reliability of LDM-based inverse problem solvers in latent space.

Findings

MCLC reduces instability in LDM-based inverse solvers.

MCLC provides more stable and reliable inverse solutions.

Compared to linear manifold methods, MCLC offers principled stabilization.

Abstract

While latent diffusion models (LDMs) have emerged as powerful priors for inverse problems, existing LDM-based solvers frequently suffer from instability. In this work, we first identify the instability as a discrepancy between the solver dynamics and stable reverse diffusion dynamics learned by the diffusion model, and show that reducing this gap stabilizes the solver. Building on this, we introduce \textit{Measurement-Consistent Langevin Corrector (MCLC)}, a theoretically grounded plug-and-play stabilization module that remedies the LDM-based inverse problem solvers through measurement-consistent Langevin updates. Compared to prior approaches that rely on linear manifold assumptions, which often fail to hold in latent space, MCLC provides a principled stabilization mechanism, leading to more stable and reliable behavior in latent space.