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

Hyoseok Lee¹Sohwi Lim¹ Eunju Cha^†2Tae-Hyun Oh^†1

¹KAIST ²Sookmyung Women’s University ^†Co-corresponding authors

ICML 2026

TL;DR: MCLC stabilizes latent diffusion inverse solvers by reducing the distributional gap in solver-induced dynamics without sacrificing measurement consistency.

Reconstruction results without and with MCLC — MCLC suppresses solver artifacts and produces cleaner, more reliable reconstructions.

MCLC corrects solver-induced dynamics toward a measurement-consistent path — Correct the dynamics while preserving the measurement.

Abstract

While latent diffusion models (LDMs) have emerged as powerful priors for inverse problems, existing LDM-based solvers frequently suffer from instability. We identify the instability as a discrepancy between solver dynamics and stable reverse diffusion dynamics learned by the diffusion model, and show that reducing this gap stabilizes the solver.

We introduce Measurement-Consistent Langevin Corrector (MCLC), a theoretically grounded plug-and-play stabilization module that remedies LDM-based inverse problem solvers through measurement-consistent Langevin updates. Unlike prior approaches relying on linear manifold assumptions, MCLC provides a principled stabilization mechanism for latent space.

Method Overview

Illustration of the MCLC projected Langevin update

After the measurement-consistency step, MCLC applies a Langevin correction in the subspace orthogonal to the measurement gradient. The correction moves deviated solver dynamics toward the diffusion model’s time-marginal distribution while preserving measurement consistency up to a controlled bound.

KL divergence with and without MCLC — MCLC narrows the KL gap between solver-induced dynamics and the learned time-marginal distribution.

Why it works

Explicit instability. We characterize instability as deviation from stable reverse diffusion dynamics.

Principled correction. Langevin dynamics monotonically reduce the distributional discrepancy.

Measurement consistency. Orthogonal projection prevents the corrector from undoing the inverse solver’s measurement update.

Qualitative Results

Measurements are fixed on the left. Drag each divider to compare Base (left) and Ours (right).

Random Inpainting

Super Resolution ×4

Motion Deblur

Gaussian Deblur

Quantitative Results

Results on FFHQ using ReSample as the base solver. MCLC particularly improves perceptual quality and reduces regional artifacts.

Task	Method	PSNR ↑	LPIPS ↓	FID ↓	P-FID ↓
Gaussian Deblur	Base	26.44	0.368	75.17	148.11
Gaussian Deblur	Ours	27.25	0.353	78.38	106.16
Motion Deblur	Base	22.45	0.635	108.14	174.52
Motion Deblur	Ours	24.24	0.588	102.02	118.87
Super Resolution	Base	26.40	0.347	70.16	133.15
Super Resolution	Ours	28.32	0.236	53.85	78.08
Random Inpainting	Base	27.27	0.374	103.17	133.80
Random Inpainting	Ours	29.35	0.235	75.65	108.27

Stabilization Effect

Beyond improving average reconstruction quality, MCLC reduces severe solver failures. The PSNR distributions consistently shift toward higher values across inverse problems.

PSNR histograms across inverse problem tasks — PSNR histograms using ReSample as the base solver. MCLC reduces the low-PSNR tail more effectively than Base and DiffStateGrad.

BibTeX

@inproceedings{
    hyoseok2026measurementconsistent,
    title={Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers},
    author={Lee Hyoseok and Sohwi Lim and Eunju Cha and Tae-Hyun Oh},
    booktitle={Forty-third International Conference on Machine Learning},
    year={2026},
    url={https://openreview.net/forum?id=QC7fOKv1jg}
}