mlsanityData to 7 Oct 2026

Training-free Linear Image Inverses via Flows

arXiv 2310.04432 ↗First posted 25 Sep 2023cs.CV cs.AI cs.LGcited by 70

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Solving inverse problems without any training involves using a pretrained generative model and making appropriate modifications to the generation process to avoid finetuning of the generative model. While recent methods have explored the use of diffusion models, they still require the manual tuning of many hyperparameters for different inverse problems. In this work, we propose a training-free method for solving linear inverse problems by using pretrained flow models, leveraging the simplicity and efficiency of Flow Matching models, using theoretically-justified weighting schemes, and thereby significantly reducing the amount of manual tuning. In particular, we draw inspiration from two main sources: adopting prior gradient correction methods to the flow regime, and a solver scheme based on conditional Optimal Transport paths. As pretrained diffusion models are widely accessible, we also show how to practically adapt diffusion models for our method. Empirically, our approach requires no problem-specific tuning across an extensive suite of noisy linear inverse problems on high-dimensional datasets, ImageNet-64/128 and AFHQ-256, and we observe that our flow-based method for solving inverse problems improves upon closely-related diffusion-based methods in most settings.

Key facts. Cited by 70 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 57 of its 78 references that are in the map. First posted on arXiv 25 Sep 2023.

Builds on

57 of 78 references.

Closest ancestors · 2

Same direction, newest first

  1. 2022Flow Matching for Generative Modeling6 Oct
  2. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 55

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2018Neural Ordinary Differential Equationscited by 3,733
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  10. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  11. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  12. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
38 more
  1. 2021Variational Diffusion Modelscited by 1,145
  2. 2017Deep Image Priorcited by 1,097
  3. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  4. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  5. 2022Denoising Diffusion Restoration Modelscited by 951
  6. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  7. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  8. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  9. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Modelcited by 574
  10. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  11. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  12. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 431
  13. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 407
  14. 2017Compressed Sensing using Generative Modelscited by 337
  15. 2023Common Diffusion Noise Schedules and Sample Steps are Flawedcited by 308
  16. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contractioncited by 306
  17. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  18. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  19. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  20. 2022Diffusion models as plug-and-play priorscited by 230
  21. 2020Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulationcited by 225
  22. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 217
  23. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  24. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 156
  25. 2022Parallel Diffusion Models of Operator and Image for Blind Inverse Problemscited by 113
  26. 2017Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problemscited by 107
  27. 2021A Study of Face Obfuscation in ImageNetcited by 83
  28. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 78
  29. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  30. 2021Intermediate Layer Optimization for Inverse Problems using Deep Generative Modelscited by 70
  31. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
  32. 2018Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guaranteescited by 58
  33. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restorationcited by 58
  34. 2020Regularization by Denoising via Fixed-Point Projection (RED-PRO)cited by 55
  35. 2020Composing Normalizing Flows for Inverse Problemscited by 48
  36. 2018Compressed Sensing with Deep Image Prior and Learned Regularizationcited by 47
  37. 2023On Kinetic Optimal Probability Paths for Generative Modelscited by 42
  38. 2023Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolutioncited by 36

50 most cited of 55 All 55 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 15; 2025: 25; 2026: 28.

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  1. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
  2. 2025Real-Time Execution of Action Chunking Flow Policiescited by 199
  3. 2024Improving the Training of Rectified Flowscited by 106
  4. 2023Guided Flows for Generative Modeling and Decision Makingcited by 99
  5. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  6. 2025Training-Time Action Conditioning for Efficient Real-Time Chunkingcited by 61
  7. 2024On conditional diffusion models for PDE simulationscited by 56
  8. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matchingcited by 50
  9. 2025On the Guidance of Flow Matchingcited by 44
  10. 2024Improved motif-scaffolding with SE(3) flow matchingcited by 43
  11. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariancecited by 42
  12. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generationcited by 38
38 more
  1. 2024Training Free Guided Flow Matching with Optimal Controlcited by 23
  2. 2025Flower: A Flow-Matching Solver for Inverse Problemscited by 23
  3. 2025Variational Control for Guidance in Diffusion Modelscited by 22
  4. 2025Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posteriorcited by 20
  5. 2026Learning Native Continuation for Action Chunking Flow Policiescited by 18
  6. 2024Fast Samplers for Inverse Problems in Iterative Refinement Modelscited by 17
  7. 2025GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Modelscited by 17
  8. 2023Guided Diffusion from Self-Supervised Diffusion Featurescited by 9
  9. 2024Bespoke Non-Stationary Solvers for Fast Sampling of Diffusion and Flow Modelscited by 9
  10. 2024Consistency Model is an Effective Posterior Sample Approximation for Diffusion Inverse Solverscited by 8
  11. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  12. 2025The Generation Phases of Flow Matching: a Denoising Perspectivecited by 6
  13. 2024Posterior sampling via Langevin dynamics based on generative priorscited by 5
  14. 2025Good Things Come in Pairs: Paired Autoencoders for Inverse Problemscited by 5
  15. 2025FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solverscited by 5
  16. 2025B'ezierFlow: Learning B'ezier Stochastic Interpolant Schedulers for Few-Step Generationcited by 5
  17. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matchingcited by 5
  18. 2025FMPlug: Plug-In Foundation Flow-Matching Priors for Inverse Problemscited by 3
  19. 2025Conditional Flow Matching for Bayesian Posterior Inferencecited by 3
  20. 2025Plug-and-Play Image Restoration with Flow Matching: A Continuous Viewpointcited by 3
  21. 2026Few-Step Diffusion Sampling Through Instance-Aware Discretizationscited by 3
  22. 2026Understanding Asynchronous Inference Methods for Vision-Language-Action Modelscited by 3
  23. 2024Flow Matching Posterior Sampling: A Training-free Conditional Generation for Flow Matchingcited by 2
  24. 2024DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problemscited by 2
  25. 2025Unsupervised Accelerated MRI Reconstruction via Ground-Truth-Free Flow Matchingcited by 2
  26. 2025Multitask Learning with Stochastic Interpolantscited by 2
  27. 2025Image Restoration via Primal Dual Hybrid Gradient and Flow Generative Modelcited by 2
  28. 2026Solving Room Impulse Response Inverse Problems Using Flow Matching with Analytic Wiener Denoisercited by 2
  29. 2026Smoother Action Chunking Flow Policy via Prior-Corrected Orthogonal Trust-Region Guidancecited by 2
  30. 2026Frequency-Guided Action Diffusion via Sub-Frequency Manifold Traversalcited by 2
  31. 2026NullFlow: One-Step Generative Reconstructioncited by 2
  32. 2025Measurement-Aligned Sampling for Inverse Problemcited by 1
  33. 2025Moir'eXNet: Adaptive Multi-Scale Demoir'eing with Linear Attention Test-Time Training and Truncated Flow Matching Priorcited 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. 2026LLM Flow Processes for Text-Conditioned Regressioncited by 1
  37. 2026Solving Inverse Problems with Flow-based Models via Model Predictive Controlcited by 1
  38. 2026Trajectory Stitching for Solving Inverse Problems with Flow-Based Modelscited by 1

50 most cited of 70 All 70 (JSON)

Similar, not cited

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  1. 2025Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving
  2. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems
  3. 2025Solving Inverse Problems with FLAIR
  4. 2024A Survey on Diffusion Models for Inverse Problems
  5. 2025A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
  6. 2026What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View
  7. 2026Consistency Regularised Gradient Flows for Inverse Problems
  8. 2024G2D2: Gradient-Guided Discrete Diffusion for Inverse Problem Solving