mlsanityData to 7 Oct 2026

Diffusion Posterior Sampling for General Noisy Inverse Problems

arXiv 2209.14687 ↗First posted 29 Sep 2022stat.ML cs.AI cs.CVcited by 1,375

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

Abstract (arXiv)

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear inverse problems in noiseless settings, which significantly under-represents the complexity of real-world problems. In this work, we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling. Interestingly, the resulting posterior sampling scheme is a blended version of diffusion sampling with the manifold constrained gradient without a strict measurement consistency projection step, yielding a more desirable generative path in noisy settings compared to the previous studies. Our method demonstrates that diffusion models can incorporate various measurement noise statistics such as Gaussian and Poisson, and also efficiently handle noisy nonlinear inverse problems such as Fourier phase retrieval and non-uniform deblurring. Code available at https://github.com/DPS2022/diffusion-posterior-sampling

Key facts. Cited by 1,375 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 21 of its 45 references that are in the map. First posted on arXiv 29 Sep 2022.

Builds on

21 of 45 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  2. 2022Denoising Diffusion Restoration Models27 Jan
  3. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 18

  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. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  6. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  7. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  8. 2016Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurringcited by 722
  9. 2022Pseudo Numerical Methods for Diffusion Models on Manifoldscited by 695
  10. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  11. 2017The Perception-Distortion Tradeoffcited by 582
  12. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
6 more
  1. 2021Score-based diffusion models for accelerated MRIcited by 308
  2. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  3. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  4. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  5. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 110
  6. 2021Explore Image Deblurring via Blur Kernel Spacecited by 58

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 11; 2023: 148; 2024: 333; 2025: 436; 2026: 447.

1,375 papers.

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  1. 2023Consistency Modelscited by 1,778
  2. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Modelcited by 574
  3. 2023Universal Guidance for Diffusion Modelscited by 426
  4. 2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 335
  5. 2023FreeDoM: Training-Free Energy-Guided Conditional Diffusion Modelcited by 290
  6. 2024NaturalSpeech 3: Zero-Shot Speech Synthesis with Factorized Codec and Diffusion Modelscited by 222
  7. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
  8. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  9. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 217
  10. 2023I2SB: Image-to-Image Schr"odinger Bridgecited by 214
  11. 2024Diffusion Model-Based Image Editing: A Surveycited by 212
  12. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Modelscited by 201
38 more
  1. 2023Image Restoration with Mean-Reverting Stochastic Differential Equationscited by 182
  2. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 180
  3. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  4. 2023DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statisticscited by 161
  5. 2022SINE: SINgle Image Editing with Text-to-Image Diffusion Modelscited by 159
  6. 2024ControlNeXt: Powerful and Efficient Control for Image and Video Generationcited by 158
  7. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  8. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 156
  9. 2023DDFM: Denoising Diffusion Model for Multi-Modality Image Fusioncited by 153
  10. 2023Manifold Preserving Guided Diffusioncited by 153
  11. 2023Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learningcited by 145
  12. 2024CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Modelscited by 138
  13. 2025Diffusion-Based Planning for Autonomous Driving with Flexible Guidancecited by 138
  14. 2023DiffTalk: Crafting Diffusion Models for Generalized Audio-Driven Portraits Animationcited by 136
  15. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problemscited by 129
  16. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
  17. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imagingcited by 126
  18. 2022Parallel Diffusion Models of Operator and Image for Blind Inverse Problemscited by 113
  19. 2023Diffusion with Forward Models: Solving Stochastic Inverse Problems Without Direct Supervisioncited by 112
  20. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 108
  21. 2023SyncDiffusion: Coherent Montage via Synchronized Joint Diffusionscited by 108
  22. 2023Diffusion Models for Image Restoration and Enhancement: A Comprehensive Surveycited by 108
  23. 2024Self-Rectifying Diffusion Sampling with Perturbed-Attention Guidancecited by 108
  24. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observationcited by 100
  25. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
  26. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  27. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 92
  28. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  29. 2023Score-based Data Assimilationcited by 91
  30. 2025Test-time Alignment of Diffusion Models without Reward Over-optimizationcited by 89
  31. 2024Arbitrary-steps Image Super-resolution via Diffusion Inversioncited by 85
  32. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Reviewcited by 82
  33. 2024NVS-Solver: Video Diffusion Model as Zero-Shot Novel View Synthesizercited by 79
  34. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusioncited by 78
  35. 2022DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstructioncited by 73
  36. 2024DITTO: Diffusion Inference-Time T-Optimization for Music Generationcited by 73
  37. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  38. 2024Diffusion Models in Low-Level Vision: A Surveycited by 73

50 most cited of 1,375 All 1,375 (JSON)

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  1. 2025Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance
  2. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling
  3. 2025DDRM-PR: Fourier Phase Retrieval using Denoising Diffusion Restoration Models
  4. 2025Plug-and-Play Posterior Sampling for Blind Inverse Problems
  5. 2026Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps
  6. 2022Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models