mlsanityData to 7 Oct 2026

Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors

arXiv 2405.18782 ↗First posted 29 May 2024eess.IV cs.CV stat.MLcited by 93

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

Abstract (arXiv)

Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods.

Key facts. Cited by 93 papers in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 55 of its 75 references that are in the map. First posted on arXiv 29 May 2024.

Builds on

55 of 75 references.

Closest ancestors · 11

Same direction, newest first

  1. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction25 Mar
  2. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problems15 Aug
  3. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  4. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  5. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  6. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  7. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  8. 2023DiffIR: Efficient Diffusion Model for Image Restoration16 Mar
  9. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  10. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  11. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 44

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  5. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  6. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  8. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  9. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  10. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  11. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  12. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
32 more
  1. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  2. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 467
  3. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 407
  4. 2021Score-based diffusion models for accelerated MRIcited by 308
  5. 2022Perception Prioritized Training of Diffusion Modelscited by 301
  6. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  7. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  8. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  9. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  10. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  11. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 195
  12. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  13. 2017Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problemscited by 107
  14. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  15. 2022Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imagingcited by 94
  16. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
  17. 2019Plug and play methods for magnetic resonance imaging (long version)cited by 75
  18. 2022DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstructioncited by 73
  19. 2022Improved analysis for a proximal algorithm for samplingcited by 72
  20. 2018An Online Plug-and-Play Algorithm for Regularized Image Reconstructioncited by 70
  21. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  22. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  23. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  24. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  25. 2018prDeep: Robust Phase Retrieval with a Flexible Deep Networkcited by 46
  26. 2023Improved dimension dependence of a proximal algorithm for samplingcited by 29
  27. 2013Phase Retrieval from Coded Diffraction Patternscited by 26
  28. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  29. 2022Probabilistic Mass Mapping with Neural Score Estimationcited by 17
  30. 2019SIMBA: Scalable Inversion in Optical Tomography using Deep Denoising Priorscited by 16
  31. 2022The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distributioncited by 11
  32. 2024Regularization by denoising: Bayesian model and Langevin-within-split Gibbs samplingcited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 14; 2025: 41; 2026: 38.

93 papers.

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By area:

  1. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  2. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  3. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  4. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  5. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generationcited by 38
  6. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  7. 2025Diffusion Tree Sampling: Scalable inference-time alignment of diffusion modelscited by 31
  8. 2026Diamond Maps: Efficient Reward Alignment via Stochastic Flow Mapscited by 26
  9. 2024Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problemscited by 18
  10. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  11. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  12. 2025GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Modelscited by 17
38 more
  1. 2024Diffusion State-Guided Projected Gradient for Inverse Problemscited by 14
  2. 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generationcited by 11
  3. 2025Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlocited by 9
  4. 2026Decoupled Diffusion Sampling for Inverse Problems on Function Spacescited by 9
  5. 2024A Unified Model for Compressed Sensing MRI Across Undersampling Patternscited by 7
  6. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  7. 2025Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problemscited by 6
  8. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  9. 2024Plug-and-Play Priors as a Score-Based Methodcited by 5
  10. 2025Enhancing Diffusion Model Stability for Image Restoration via Gradient Managementcited by 5
  11. 2024Machine learning-enabled velocity model building with uncertainty quantificationcited by 4
  12. 2025Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolationcited by 4
  13. 2025PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problemscited by 4
  14. 2026Calibrated Test-Time Guidance for Bayesian Inferencecited by 4
  15. 2025STeP: A Framework for Solving Scientific Video Inverse Problems with Spatiotemporal Diffusion Priorscited by 3
  16. 2025Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problemscited by 3
  17. 2025Super-Resolution Optical Coherence Tomography Using Diffusion Model-Based Plug-and-Play Priorscited by 3
  18. 2025Dual Ascent Diffusion for Inverse Problemscited by 3
  19. 2025FNOPE: Simulation-based inference on function spaces with Fourier Neural Operatorscited by 3
  20. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithmcited by 3
  21. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 3
  22. 2025DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealingcited by 3
  23. 2025Plug-and-Play Image Restoration with Flow Matching: A Continuous Viewpointcited by 3
  24. 2025PSI3D: Plug-and-Play 3D Stochastic Inference with Slice-wise Latent Diffusion Priorcited by 3
  25. 2026Sample-efficient evidence estimation of score based priors for model selectioncited by 3
  26. 2026Stochastic Generative Plug-and-Play Priorscited by 3
  27. 2024Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximationcited by 2
  28. 2025Benchmarking Diffusion Annealing-Based Bayesian Inverse Problem Solverscited by 2
  29. 2025Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problemscited by 2
  30. 2025Learning Single Index Models with Diffusion Priorscited by 2
  31. 2025Plug-and-Play Posterior Sampling for Blind Inverse Problemscited by 2
  32. 2025Plug-and-Play Latent Diffusion for Electromagnetic Inverse Scattering with Application to Brain Imagingcited by 2
  33. 2025Local MAP Sampling for Diffusion Modelscited by 2
  34. 2025Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Samplingcited by 2
  35. 2025Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Modelscited by 2
  36. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 2
  37. 2024ADOBI: Adaptive Diffusion Bridge For Blind Inverse Problems with Application to MRI Reconstructioncited by 1
  38. 2025Solving Inverse Problems using Diffusion with Iterative Colored Renoisingcited by 1

50 most cited of 93 All 93 (JSON)

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Close in wording, no citation either way

  1. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  2. 2025Diffusion models for inverse problems
  3. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems
  4. 2023Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior
  5. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling
  6. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  7. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling
  8. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion models