Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers
This addresses instability issues for users of latent diffusion models in inverse problems, though it appears incremental as it builds on existing solvers.
The authors tackled instability in latent diffusion model-based inverse problem solvers by identifying a discrepancy in dynamics and introduced the Measurement-Consistent Langevin Corrector (MCLC) to stabilize them, resulting in more stable and reliable behavior in latent space.
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.