mlsanityData to 7 Oct 2026

PnP-Flow: Plug-and-Play Image Restoration with Flow Matching

arXiv 2410.02423 ↗First posted 3 Oct 2024cs.CV cs.LGcited by 92

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

Abstract (arXiv)

In this paper, we introduce Plug-and-Play (PnP) Flow Matching, an algorithm for solving imaging inverse problems. PnP methods leverage the strength of pre-trained denoisers, often deep neural networks, by integrating them in optimization schemes. While they achieve state-of-the-art performance on various inverse problems in imaging, PnP approaches face inherent limitations on more generative tasks like inpainting. On the other hand, generative models such as Flow Matching pushed the boundary in image sampling yet lack a clear method for efficient use in image restoration. We propose to combine the PnP framework with Flow Matching (FM) by defining a time-dependent denoiser using a pre-trained FM model. Our algorithm alternates between gradient descent steps on the data-fidelity term, reprojections onto the learned FM path, and denoising. Notably, our method is computationally efficient and memory-friendly, as it avoids backpropagation through ODEs and trace computations. We evaluate its performance on denoising, super-resolution, deblurring, and inpainting tasks, demonstrating superior results compared to existing PnP algorithms and Flow Matching based state-of-the-art methods.

Key facts. Cited by 92 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 60 of its 78 references that are in the map. First posted on arXiv 3 Oct 2024.

Builds on

60 of 78 references.

Closest ancestors · 9

Same direction, newest first

  1. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  2. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  3. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction25 Mar
  4. 2023Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance27 Dec
  5. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  6. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  7. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  8. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  9. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 51

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  7. 2022Flow Matching for Generative Modelingcited by 5,426
  8. 2018Neural Ordinary Differential Equationscited by 3,733
  9. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  10. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  11. 2016Density estimation using Real NVPcited by 2,029
  12. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
38 more
  1. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  2. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  3. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  4. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  5. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  6. 2017The Perception-Distortion Tradeoffcited by 582
  7. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 467
  8. 2017Compressed Sensing using Generative Modelscited by 337
  9. 2024Discrete Flow Matchingcited by 301
  10. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transportcited by 277
  11. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  12. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  13. 2022Diffusion models as plug-and-play priorscited by 230
  14. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  15. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 182
  16. 2023Manifold Preserving Guided Diffusioncited by 153
  17. 2024D-Flow: Differentiating through Flows for Controlled Generationcited by 115
  18. 2024Dirichlet Flow Matching with Applications to DNA Sequence Designcited by 110
  19. 2017Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problemscited by 107
  20. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  21. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistencycited by 101
  22. 2019Invertible generative models for inverse problems: mitigating representation error and dataset biascited by 93
  23. 2023Error Bounds for Flow Matching Methodscited by 88
  24. 2023Minimizing Trajectory Curvature of ODE-based Generative Modelscited by 87
  25. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
  26. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  27. 2018An Online Plug-and-Play Algorithm for Regularized Image Reconstructioncited by 70
  28. 2023Training-free Linear Image Inverses via Flowscited by 70
  29. 2024Fisher Flow Matching for Generative Modeling over Discrete Datacited by 68
  30. 2020Learning Maximally Monotone Operators for Image Recoverycited by 62
  31. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matchingcited by 50
  32. 2015From Facial Parts Responses to Face Detection: A Deep Learning Approachcited by 42
  33. 2020Convolutional Proximal Neural Networks and Plug-and-Play Algorithmscited by 36
  34. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 34
  35. 2021Deep Unfolding with Normalizing Flow Priors for Inverse Problemscited by 23
  36. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  37. 2023Provably Convergent Plug-and-Play Quasi-Newton Methodscited by 15
  38. 2023Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problemscited by 14

50 most cited of 51 All 51 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 45; 2026: 44.

92 papers.

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  1. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problemscited by 65
  2. 2025On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticitycited by 48
  3. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generationcited by 38
  4. 2025UniEdit-Flow: Unleashing Inversion and Editing in the Era of Flow Modelscited by 38
  5. 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translationcited by 36
  6. 2025Flower: A Flow-Matching Solver for Inverse Problemscited by 23
  7. 2025The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generationcited by 16
  8. 2025On the Relation between Rectified Flows and Optimal Transportcited by 15
  9. 2025Source-Guided Flow Matchingcited by 11
  10. 2025ARFlow: Human Action-Reaction Flow Matching with Physical Guidancecited by 7
  11. 2025Telegrapher's Generative Model via Kac Flowscited by 7
  12. 2025MRI Super-Resolution with Deep Learning: A Comprehensive Surveycited by 7
38 more
  1. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  2. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  3. 2025The Generation Phases of Flow Matching: a Denoising Perspectivecited by 6
  4. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion modelscited by 5
  5. 2025Optimal Transport for Rectified Flow Image Editing: Unifying Inversion-Based and Direct Methodscited by 5
  6. 2025Prompt-Guided Dual Latent Steering for Inversion Problemscited by 5
  7. 2025FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solverscited by 5
  8. 2025Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidancecited by 5
  9. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matchingcited by 5
  10. 2025Benchmarking GANs, Diffusion Models, and Flow Matching for T1w-to-T2w MRI Translationcited by 4
  11. 2026RAW-Flow: Advancing RGB-to-RAW Image Reconstruction with Deterministic Latent Flow Matchingcited by 4
  12. 2026ProjFlow: Projection Sampling with Flow Matching for Zero-Shot Exact Spatial Motion Controlcited by 4
  13. 2024Plug-and-Play Half-Quadratic Splitting for Ptychographycited by 3
  14. 2025FMPlug: Plug-In Foundation Flow-Matching Priors for Inverse Problemscited by 3
  15. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithmcited by 3
  16. 2025Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysiscited by 3
  17. 2025FlowOpt: Fast Optimization Through Whole Flow Processes for Training-Free Editingcited by 3
  18. 2025Plug-and-Play Image Restoration with Flow Matching: A Continuous Viewpointcited by 3
  19. 2025CTSR: Controllable Fidelity-Realness Trade-off Distillation for Real-World Image Super Resolutioncited by 2
  20. 2025Efficient Image Restoration with State-Dependent Forward Diffusioncited by 2
  21. 2025Multitask Learning with Stochastic Interpolantscited by 2
  22. 2025Provable Mixed-Noise Learning with Flow-Matchingcited by 2
  23. 2025LVTINO: LAtent Video consisTency INverse sOlver for High Definition Video Restorationcited by 2
  24. 2025A Mathematical Explanation of Transformerscited by 2
  25. 2025Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solvingcited by 2
  26. 2025Image Restoration via Primal Dual Hybrid Gradient and Flow Generative Modelcited by 2
  27. 2026Solving Room Impulse Response Inverse Problems Using Flow Matching with Analytic Wiener Denoisercited by 2
  28. 2026Beyond MMSE: Enhancing PnP Restoration with ProxiMAPcited by 2
  29. 2026NullFlow: One-Step Generative Reconstructioncited by 2
  30. 2025Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fieldscited by 1
  31. 2025Moir'eXNet: Adaptive Multi-Scale Demoir'eing with Linear Attention Test-Time Training and Truncated Flow Matching Priorcited by 1
  32. 2025An invertible generative model for forward and inverse problemscited by 1
  33. 2025Integrating Reweighted Least Squares with Plug-and-Play Diffusion Priors for Noisy Image Restorationcited by 1
  34. 2025Restora-Flow: Mask-Guided Image Restoration with Flow Matchingcited by 1
  35. 2025FlowSteer: Conditioning Flow Field for Consistent Image Restorationcited by 1
  36. 2026Channel Estimation in MIMO Systems Using Flow Matching Modelscited by 1
  37. 2026ProFlow: Zero-Shot Physics-Consistent Sampling via Proximal Flow Guidancecited by 1
  38. 2026Solving Inverse Problems with Flow-based Models via Model Predictive Controlcited by 1

50 most cited of 92 All 92 (JSON)

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  1. 2024Plug-and-Play image restoration with Stochastic deNOising REgularization
  2. 2026Stochastic Generative Plug-and-Play Priors
  3. 2024Plug-and-Play Priors as a Score-Based Method
  4. 2025Multi Task Denoiser Training for Solving Linear Inverse Problems ↗
  5. 2025Viscosity Stabilized Plug-and-Play Reconstruction ↗
  6. 2024DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems
  7. 2024Fast Samplers for Inverse Problems in Iterative Refinement Models
  8. 2026Flow Map Denoisers: Traversing the Distortion-Perception Plane for Inverse Problems