mlsanityData to 14 Oct 2026

Learning few-step posterior samplers by unfolding and distillation of diffusion models

arXiv 2507.02686 ↗First posted 3 Jul 2025cs.CV cs.LGcited by 6

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

Abstract (arXiv)

Diffusion models (DMs) have emerged as powerful image priors in Bayesian computational imaging. Two primary strategies have been proposed for leveraging DMs in this context: Plug-and-Play methods, which are zero-shot and highly flexible but rely on approximations; and specialized conditional DMs, which achieve higher accuracy and faster inference for specific tasks through supervised training. In this work, we introduce a novel framework that integrates deep unfolding and model distillation to transform a DM image prior into a few-step conditional model for posterior sampling. A central innovation of our approach is the unfolding of a Markov chain Monte Carlo (MCMC) algorithm - specifically, the recently proposed LATINO Langevin sampler (Spagnoletti et al., 2025) - representing the first known instance of deep unfolding applied to a Monte Carlo sampling scheme. We demonstrate our proposed unfolded and distilled samplers through extensive experiments and comparisons with the state of the art, where they achieve excellent accuracy and computational efficiency, while retaining the flexibility to adapt to variations in the forward model at inference time.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 52 of its 67 references that are in the map. First posted on arXiv 3 Jul 2025.

Builds on

52 of 67 references.

Closest ancestors · 14

Same direction, newest first

  1. 2025Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problems16 May
  2. 2025InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problems2 Apr
  3. 2025LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimization16 Mar
  4. 2024Zero-Shot Image Restoration Using Few-Step Guidance of Consistency Models (and Beyond)29 Dec
  5. 2024Variational Diffusion Posterior Sampling with Midpoint Guidance13 Oct
  6. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matching3 Oct
  7. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  8. 2024Empirical Bayesian image restoration by Langevin sampling with a denoising diffusion implicit prior6 Sep
  9. 2024CoSIGN: Few-Step Guidance of ConSIstency Model to Solve General INverse Problems17 Jul
  10. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problems31 May
  11. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  12. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
2 more
  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  2. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 38

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  3. 2020Denoising Diffusion Implicit Modelscited by 9,781
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,498
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  7. 2022Flow Matching for Generative Modelingcited by 5,702
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  9. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  10. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,054
  11. 2023Consistency Modelscited by 1,822
  12. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,355
26 more
  1. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  2. 2022On Distillation of Guided Diffusion Modelscited by 725
  3. 2024Improved Distribution Matching Distillation for Fast Image Synthesiscited by 684
  4. 2018Which Training Methods for GANs do actually Converge?cited by 679
  5. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 470
  6. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 459
  7. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 421
  8. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speedcited by 348
  9. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 291
  10. 2023I2SB: Image-to-Image Schr"odinger Bridgecited by 218
  11. 2023LCM-LoRA: A Universal Stable-Diffusion Acceleration Modulecited by 211
  12. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 97
  13. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 84
  14. 2014Learning to Deblurcited by 66
  15. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  16. 2013Proximal Markov chain Monte Carlo algorithmscited by 46
  17. 2022Learned reconstruction methods with convergence guaranteescited by 46
  18. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 42
  19. 2021Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmscited by 24
  20. 2023Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problemscited by 17
  21. 2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
  22. 2021Conditional Frechet Inception Distancecited by 16
  23. 2022The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distributioncited by 11
  24. 2022A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problemscited by 9
  25. 2023Normalizing flow sampling with Langevin dynamics in the latent spacecited by 7
  26. 2024Uncertainty quantification for fast reconstruction methods using augmented equivariant bootstrap: Application to radio interferometrycited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 4.

6 papers.

  1. 2025LVTINO: LAtent Video consisTency INverse sOlver for High Definition Video Restorationcited by 2
  2. 2026Consistency Regularised Gradient Flows for Inverse Problemscited by 2
  3. 2026Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inferencecited by 1
  4. 2025Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurementscited by 0
  5. 2026Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior samplingcited by 0
  6. 2026BAM! Bayesian Anything Model: a foundation model for generative computational imagingcited by 0

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Close in wording, no citation either way

  1. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  2. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors
  3. 2024Think Twice Before You Act: Improving Inverse Problem Solving With MCMC
  4. 2023Accelerating Markov Chain Monte Carlo sampling with diffusion models
  5. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey
  6. 2026Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
  7. 2024Bayesian computation with generative diffusion models by Multilevel Monte Carlo
  8. 2025A Mixture-Based Framework for Guiding Diffusion Models