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 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.

Many scientific and engineering problems involve recovering hidden information from incomplete or corrupted observations. Because the observations are often not enough to uniquely determine the answer, recent methods use powerful generative models, especially diffusion models, as prior knowledge about what realistic solutions should look like. However, when these models are used inside inverse problem solvers, the reconstruction process can become unstable, leading to artifacts or unreliable results. This work studies why such instability happens and how to reduce it. We show that an unstable solver can be understood as one whose reconstruction path drifts away from the generation path learned by the diffusion model. To address this, we introduce Measurement-Consistent Langevin Corrector (MCLC). MCLC gently corrects the solver toward the diffusion model’s learned generation process, while still preserving agreement with the actual observations. By stabilizing existing solvers without redesigning them, MCLC can help make latent diffusion-based inverse problem solving more reliable across different tasks and domains. More broadly, our work suggests a practical and principled way to build generative reconstruction systems that are not only powerful, but also more stable and trustworthy.