mlsanityData to 13 Oct 2026

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

arXiv 2601.04791 ↗First posted 8 Jan 2026cs.CV cs.LGcited by 1

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

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 textitMeasurement-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.

Key facts. Cited by 1 paper in the map (data through 13 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 39 of its 53 references that are in the map. First posted on arXiv 8 Jan 2026.

Builds on

39 of 53 references.

Closest ancestors · 16

Same direction, newest first

  1. 2025SILO: Solving Inverse Problems with Latent Operators20 Jan
  2. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems6 Oct
  3. 2024Diffusion State-Guided Projected Gradient for Inverse Problems4 Oct
  4. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  5. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  6. 2024Fast Samplers for Inverse Problems in Iterative Refinement Models27 May
  7. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion1 Dec
  8. 2023Regularization by Texts for Latent Diffusion Inverse Solvers27 Nov
  9. 2023Prompt-tuning latent diffusion models for inverse problems2 Oct
  10. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  11. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  12. 2023DiracDiffusion: Denoising and Incremental Reconstruction with Assured Data-Consistency25 Mar
4 more
  1. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  2. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  3. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  4. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 23

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,952
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,777
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,028
  4. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,000
  5. 2017Deep Image Priorcited by 1,097
  6. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  7. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Modelscited by 444
  8. 2023Universal Guidance for Diffusion Modelscited by 434
  9. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 304
  10. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  11. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 207
  12. 2023Manifold Preserving Guided Diffusioncited by 156
11 more
  1. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 145
  2. 2022Any-resolution Training for High-resolution Image Synthesiscited by 72
  3. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problemscited by 67
  4. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  5. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generationcited by 38
  6. 2020Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learningcited by 33
  7. 2024Understanding and Improving Training-free Loss-based Diffusion Guidancecited by 31
  8. 2023Robust Unsupervised StyleGAN Image Restorationcited by 14
  9. 2023Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problemscited by 14
  10. 2024DC-Solver: Improving Predictor-Corrector Diffusion Sampler via Dynamic Compensationcited by 11
  11. 2025MEAT: Multiview Diffusion Model for Human Generation on Megapixels with Mesh Attentioncited by 8

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Measured-Subspace Consistency: A Plug-and-Play Operator for Diffusion Posterior Sampling in Accelerated MRI Reconstructioncited by 0

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  1. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems
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  4. 2025PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problems
  5. 2024Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics
  6. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems
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  8. 2023Solving Inverse Physics Problems with Score Matching