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

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 $\mathit{\text{Measurement-Consistent}}\mathit{\text{Langevin}}\mathit{\text{Corrector}}\mathit{\text{(MCLC)}}$, 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.