mlsanityData to 7 Oct 2026

Parallel Diffusion Models of Operator and Image for Blind Inverse Problems

arXiv 2211.10656 ↗First posted 19 Nov 2022cs.CV cs.LG stat.MLcited by 113

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

Abstract (arXiv)

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be explored. In this work, we show that we can indeed solve a family of blind inverse problems by constructing another diffusion prior for the forward operator. Specifically, parallel reverse diffusion guided by gradients from the intermediate stages enables joint optimization of both the forward operator parameters as well as the image, such that both are jointly estimated at the end of the parallel reverse diffusion procedure. We show the efficacy of our method on two representative tasks -- blind deblurring, and imaging through turbulence -- and show that our method yields state-of-the-art performance, while also being flexible to be applicable to general blind inverse problems when we know the functional forms.

Key facts. Cited by 113 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 31 of its 64 references that are in the map. First posted on arXiv 19 Nov 2022.

Builds on

31 of 64 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  2. 2022JPEG Artifact Correction using Denoising Diffusion Restoration Models23 Sep
  3. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  4. 2022Denoising Diffusion Restoration Models27 Jan
  5. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 26

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  4. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  5. 2022Video Diffusion Modelscited by 2,280
  6. 2021Restormer: Efficient Transformer for High-Resolution Image Restorationcited by 1,618
  7. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  8. 2020Pre-Trained Image Processing Transformercited by 891
  9. 2021Uformer: A General U-Shaped Transformer for Image Restorationcited by 864
  10. 2021Multi-Stage Progressive Image Restorationcited by 813
  11. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  12. 2017The Perception-Distortion Tradeoffcited by 582
14 more
  1. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  2. 2017DeblurGAN: Blind Motion Deblurring Using Conditional Adversarial Networkscited by 366
  3. 2019DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Bettercited by 361
  4. 2021Score-based diffusion models for accelerated MRIcited by 308
  5. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  6. 2015Learning a Convolutional Neural Network for Non-uniform Motion Blur Removalcited by 148
  7. 2019Neural Blind Deconvolution Using Deep Priorscited by 113
  8. 2014Learning to Deblurcited by 66
  9. 2022Single Frame Atmospheric Turbulence Mitigation: A Benchmark Study and A New Physics-Inspired Transformer Modelcited by 37
  10. 2020Image Reconstruction of Static and Dynamic Scenes through Anisoplanatic Turbulencecited by 30
  11. 2018Subsampled Turbulence Removal Networkcited by 22
  12. 2022Tilt-then-Blur or Blur-then-Tilt? Clarifying the Atmospheric Turbulence Modelcited by 17
  13. 2018Learning a Discriminative Prior for Blind Image Deblurringcited by 15
  14. 2022Accelerated Motion Correction with Deep Generative Diffusion Modelscited by 12

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 25; 2024: 34; 2025: 40; 2026: 14.

113 papers.

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  1. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 217
  2. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  3. 2023Diffusion Models for Image Restoration and Enhancement: A Comprehensive Surveycited by 108
  4. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  5. 2023Training-free Linear Image Inverses via Flowscited by 70
  6. 2023Residual Denoising Diffusion Modelscited by 68
  7. 2024DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Modelscited by 60
  8. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restorationcited by 58
  9. 2023Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Modelscited by 53
  10. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  11. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  12. 2023WaveDM: Wavelet-Based Diffusion Models for Image Restorationcited by 46
38 more
  1. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  2. 2023Image Restoration Through Generalized Ornstein-Uhlenbeck Bridgecited by 41
  3. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generationcited by 38
  4. 2023Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolutioncited by 36
  5. 2023Regularization by Texts for Latent Diffusion Inverse Solverscited by 31
  6. 2024Blind Image Restoration via Fast Diffusion Inversioncited by 29
  7. 2024Token Caching for Diffusion Transformer Accelerationcited by 29
  8. 2024Conditional Image Synthesis with Diffusion Models: A Surveycited by 29
  9. 2023Physics-Driven Turbulence Image Restoration with Stochastic Refinementcited by 24
  10. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problemscited by 23
  11. 2023Controllable Inversion of Black-Box Face Recognition Models via Diffusioncited by 22
  12. 2023Accelerating Diffusion Models for Inverse Problems through Shortcut Samplingcited by 21
  13. 2023Blind Audio Bandwidth Extension: A Diffusion-Based Zero-Shot Approachcited by 21
  14. 2024Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problemscited by 18
  15. 2025Diffusion models for inverse problemscited by 15
  16. 2025Residual Diffusion Bridge Model for Image Restorationcited by 14
  17. 2024Osmosis: RGBD Diffusion Prior for Underwater Image Restorationcited by 13
  18. 2024A Diffusion-Based Generative Equalizer for Music Restorationcited by 12
  19. 2024Adaptive Compressed Sensing with Diffusion-Based Posterior Samplingcited by 12
  20. 2023Diffusion Reflectance Map: Single-Image Stochastic Inverse Rendering of Illumination and Reflectancecited by 11
  21. 2024Unsupervised Blind Joint Dereverberation and Room Acoustics Estimation with Diffusion Modelscited by 11
  22. 2024Blind Inversion using Latent Diffusion Priorscited by 10
  23. 2024Diff-Shadow: Global-guided Diffusion Model for Shadow Removalcited by 10
  24. 2024Deep Learning Techniques for Atmospheric Turbulence Removal: A Reviewcited by 10
  25. 2025Tackling Hallucination from Conditional Models for Medical Image Reconstruction with DynamicDPScited by 10
  26. 2023Diffusion Posterior Sampling for Informed Single-Channel Dereverberationcited by 9
  27. 2024BUDDy: Single-Channel Blind Unsupervised Dereverberation with Diffusion Modelscited by 9
  28. 2024Pi-fusion: Physics-informed diffusion model for learning fluid dynamicscited by 9
  29. 2025InterLCM: Low-Quality Images as Intermediate States of Latent Consistency Models for Effective Blind Face Restorationcited by 9
  30. 2023Block Coordinate Plug-and-Play Methods for Blind Inverse Problemscited by 8
  31. 2023Fast and Stable Diffusion Inverse Solver with History Gradient Updatecited by 8
  32. 2023Denoising Heat-inspired Diffusion with Insulators for Collision Free Motion Planningcited by 8
  33. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlocited by 7
  34. 2025ArrayDPS: Unsupervised Blind Speech Separation with a Diffusion Priorcited by 7
  35. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  36. 2023Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusioncited by 6
  37. 2023Diffusion Posterior Illumination for Ambiguity-aware Inverse Renderingcited by 6
  38. 2024DeTurb: Atmospheric Turbulence Mitigation with Deformable 3D Convolutions and 3D Swin Transformerscited by 6

50 most cited of 113 All 113 (JSON)

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  1. 2025PRISM: Probabilistic and Robust Inverse Solver with Measurement-Conditioned Diffusion Prior for Blind Inverse Problems
  2. 2024Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problems
  3. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems
  4. 2024Inverse Problems with Diffusion Models: A MAP Estimation Perspective
  5. 2024Enhancing and Accelerating Diffusion-Based Inverse Problem Solving through Measurements Optimization
  6. 2026Principled Design of Diffusion-based Optimizers for Inverse Problems
  7. 2025Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolation
  8. 2026FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems