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

Lee Hyoseok, Sohwi Lim, Eunju Cha, Tae-Hyun Oh

Keywords: Inverse Problem, Latent Diffusion Model, Diffusion-based Inverse Problem Solver, Instability

TL;DR: We identify instability in latent diffusion inverse problem solvers as a gap in reverse dynamics, and propose a plug-and-play module that stabilizes existing solvers without sacrificing data fidelity.

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 _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.

Submission Number: 70