mlsanityData to 7 Oct 2026

GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration

arXiv 2301.12686 ↗First posted 30 Jan 2023cs.LG cs.AI cs.CVcited by 58

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

Abstract (arXiv)

Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine-tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.

Key facts. Cited by 58 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 39 of its 68 references that are in the map. First posted on arXiv 30 Jan 2023.

Builds on

39 of 68 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Parallel Diffusion Models of Operator and Image for Blind Inverse Problems19 Nov
  2. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  3. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 36

  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. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  9. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  10. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  11. 2017Mixed Precision Trainingcited by 1,135
  12. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
24 more
  1. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  2. 2021Multi-Stage Progressive Image Restorationcited by 813
  3. 2016CNN Architectures for Large-Scale Audio Classificationcited by 701
  4. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  5. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  6. 2018SDR - half-baked or well done?cited by 420
  7. 2019DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Bettercited by 361
  8. 2022MAXIM: Multi-Axis MLP for Image Processingcited by 301
  9. 2016Learning Representations for Automatic Colorizationcited by 251
  10. 2017Image reconstruction by domain transform manifold learningcited by 231
  11. 2018Fr'echet Audio Distance: A Metric for Evaluating Music Enhancement Algorithmscited by 221
  12. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  13. 2016Semantic Image Inpainting with Deep Generative Modelscited by 156
  14. 2019Neural Blind Deconvolution Using Deep Priorscited by 113
  15. 2018The Singular Values of Convolutional Layerscited by 95
  16. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 78
  17. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
  18. 2021Interspeech 2021 Deep Noise Suppression Challengecited by 43
  19. 2020Solving Inverse Problems with a Flow-based Noise Modelcited by 31
  20. 2022Unsupervised vocal dereverberation with diffusion-based generative modelscited by 18
  21. 2020NHSS: A Speech and Singing Parallel Databasecited by 16
  22. 2022Music Enhancement via Image Translation and Vocodingcited by 11
  23. 2021Reverb Conversion of Mixed Vocal Tracks Using an End-to-end Convolutional Deep Neural Networkcited by 8
  24. 2018An Unsupervised Approach to Solving Inverse Problems using Generative Adversarial Networkscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 12; 2024: 24; 2025: 16; 2026: 6.

58 papers.

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  1. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
  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. 2024Arbitrary-steps Image Super-resolution via Diffusion Inversioncited by 85
  5. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  6. 2023Training-free Linear Image Inverses via Flowscited by 70
  7. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problemscited by 65
  8. 2024Efficient Diffusion Model for Image Restoration by Residual Shiftingcited by 64
  9. 2023WaveDM: Wavelet-Based Diffusion Models for Image Restorationcited by 46
  10. 2023Image Restoration Through Generalized Ornstein-Uhlenbeck Bridgecited by 41
  11. 2024Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restorationcited by 32
  12. 2024Blind Image Restoration via Fast Diffusion Inversioncited by 29
38 more
  1. 2023Blind Audio Bandwidth Extension: A Diffusion-Based Zero-Shot Approachcited by 21
  2. 2025UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Controlcited by 18
  3. 2023DPoser: Diffusion Model as Robust 3D Human Pose Priorcited by 17
  4. 2023Uncertainty Quantification via Neural Posterior Principal Componentscited by 16
  5. 2025Diffusion models for inverse problemscited by 15
  6. 2024Osmosis: RGBD Diffusion Prior for Underwater Image Restorationcited by 13
  7. 2024Residual-Conditioned Optimal Transport: Towards Structure-Preserving Unpaired and Paired Image Restorationcited by 13
  8. 2024Adaptive Compressed Sensing with Diffusion-Based Posterior Samplingcited by 12
  9. 2024Unsupervised Blind Joint Dereverberation and Room Acoustics Estimation with Diffusion Modelscited by 11
  10. 2023On the Equivalence of Consistency-Type Models: Consistency Models, Consistent Diffusion Models, and Fokker-Planck Regularizationcited by 10
  11. 2024Blind Inversion using Latent Diffusion Priorscited by 10
  12. 2024BUDDy: Single-Channel Blind Unsupervised Dereverberation with Diffusion Modelscited by 9
  13. 2023Zero-Shot Duet Singing Voices Separation with Diffusion Modelscited by 6
  14. 2025Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problemscited by 6
  15. 2024Listening to the Noise: Blind Denoising with Gibbs Diffusioncited by 5
  16. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Samplingcited by 5
  17. 2025Unsupervised Imaging Inverse Problems with Diffusion Distribution Matchingcited by 5
  18. 2024Burst Super-Resolution with Diffusion Models for Improving Perceptual Qualitycited by 3
  19. 2024Training-Free Multi-User Generative Semantic Communications via Null-Space Diffusion Samplingcited by 3
  20. 2025INDIGO+: A Unified INN-Guided Probabilistic Diffusion Algorithm for Blind and Non-Blind Image Restorationcited by 3
  21. 2025Diffusion Image Priorcited by 3
  22. 2024Towards Unsupervised Blind Face Restoration using Diffusion Priorcited by 2
  23. 2025Plug-and-Play Posterior Sampling for Blind Inverse Problemscited by 2
  24. 2025Efficient Burst Super-Resolution with One-step Diffusioncited by 2
  25. 2025Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Modelscited by 2
  26. 2025SFBD-OMNI: Bridge models for lossy measurement restoration with limited clean samplescited by 2
  27. 2024Manifold-Guided Lyapunov Control with Diffusion Modelscited by 1
  28. 2024ADOBI: Adaptive Diffusion Bridge For Blind Inverse Problems with Application to MRI Reconstructioncited by 1
  29. 2024Blind Inverse Problem Solving Made Easy by Text-to-Image Latent Diffusioncited by 1
  30. 2024Aberration Correcting Vision Transformers for High-Fidelity Metalens Imagingcited by 1
  31. 2025Invert2Restore: Zero-Shot Degradation-Blind Image Restorationcited by 1
  32. 2025Double Blind Imaging with Generative Modelingcited by 1
  33. 2025A Unified and Fast-Sampling Diffusion Bridge Framework via Stochastic Optimal Controlcited by 1
  34. 2025Restoring Noisy Demonstration for Imitation Learning With Diffusion Modelscited by 1
  35. 2026Outlier-Robust Diffusion Solvers for Inverse Problemscited by 1
  36. 2024Denoising Diffusion Restoration Tackles Forward and Inverse Problems for the Laplace Operatorcited by 0
  37. 2024CODE: Confident Ordinary Differential Editingcited by 0
  38. 2024Fundus image enhancement through direct diffusion bridgescited by 0

50 most cited of 58 All 58 (JSON)

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  1. 2025A Mixture-Based Framework for Guiding Diffusion Models
  2. 2023Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution
  3. 2026A Gibbs posterior sampler for inverse problem based on prior diffusion model
  4. 2026Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
  5. 2026Provable diffusion-based posterior sampling for linear inverse problems via DDIM
  6. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  7. 2025Normalization-equivariant Diffusion Models: Learning Posterior Samplers From Noisy And Partial Measurements
  8. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithm