Measurement-Consistent Langevin Corrector: A Remedy for Latent Diffusion Inverse Solvers

TL;DR

The paper addresses instability in latent-diffusion inverse solvers by identifying a gap between the solver's reverse diffusion dynamics and the true reverse diffusion process. It introduces Measurement-Consistent Langevin Corrector (MCLC), a plug-and-play, projection-based Langevin correction that preserves measurement fidelity while driving the latent dynamics toward the true stationary distribution. Empirically, MCLC yields consistent improvements across multiple latent solvers and tasks on FFHQ and ImageNet, with modest compute overhead and strong artifact reduction, including blob artifacts linked to latent-scale-outliers. The work also provides theoretical guarantees and extensive analyses of artifacts, demonstrating MCLC as a robust step toward reliable zero-shot inverse diffusion solvers.

Abstract

With recent advances in generative models, diffusion models have emerged as powerful priors for solving inverse problems in each domain. Since Latent Diffusion Models (LDMs) provide generic priors, several studies have explored their potential as domain-agnostic zero-shot inverse solvers. Despite these efforts, existing latent diffusion inverse solvers suffer from their instability, exhibiting undesirable artifacts and degraded quality. In this work, we first identify the instability as a discrepancy between the solver's and true reverse diffusion dynamics, 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 correction module that remedies the LDM-based inverse solvers through measurement-consistent Langevin updates. Compared to prior approaches that rely on linear manifold assumptions, which often do not hold in latent space, MCLC operates without this assumption, leading to more stable and reliable behavior. We experimentally demonstrate the effectiveness of MCLC and its compatibility with existing solvers across diverse image restoration tasks. Additionally, we analyze blob artifacts and offer insights into their underlying causes. We highlight that MCLC is a key step toward more robust zero-shot inverse problem solvers.

Figures (26)

• Figure 1: Reconstructed results without and with our proposed Measurement-Consistent Langevin Corrector (MCLC). While naive solvers rout2023psldsong2023resample fail to recover images faithfully, our plug-and-play MCLC successfully corrects latent diffusion inverse solvers by reducing the gap to the true reverse sampling process. MCLC is simple yet effective in stabilizing latent diffusion inverse solvers, thereby mitigating artifacts and improving quality.
• Figure 2: Reverse diffusion dynamics of PSLD. We visualize the reverse sampling trajectory of $\bm{z}_{0\vert t}$ for the latent diffusion inverse solver (PSLD rout2023psld). The naive dynamics of solver exhibits undesirable artifacts (first row), whereas the solver corrected with MCLC yields cleaner and more structured latents (second row). For clarity, only the fourth channel is visualized.
• Figure 3: KL divergence between the time-evolving distribution of solver and the true reverse diffusion distribution across timesteps. The clear gap (red line) supports our assumption, and MCLC effectively narrows it (purple line).
• Figure 4: Illustration of MCLC. After the measurement consistency step, MCLC is applied to mitigate the off-stationarity. MCLC performs Langevin updates on the subspace orthogonal to the measurement gradient, thereby preserving measurement consistency during the correction process. Our proposed corrector effectively alleviates the problematic latent updates.
• Figure 5: Qualitative comparison of base latent diffusion inverse solvers and their plug-in versions with DiffStateGrad zirvi2025state and MCLC (ours). Proposed MCLC effectively alleviates artifacts and enhances reconstruction quality. The baseline used for visualization is ReSample (top two rows) and PSLD (bottom two rows).

Theorems & Definitions (6)

• Proposition 1: Langevin Corrector
• Remark 1: Vanilla corrector may disturb measurement consistency
• Theorem 1
• Proposition 1: Langevin Corrector
• Lemma 1
• Theorem 1