mlsanityData to 7 Oct 2026

Stochastic Image Denoising by Sampling from the Posterior Distribution

arXiv 2101.09552 ↗First posted 23 Jan 2021eess.IV cs.CVcited by 45

Not on the map. Why?

Cited by 29 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Image denoising is a well-known and well studied problem, commonly targeting a minimization of the mean squared error (MSE) between the outcome and the original image. Unfortunately, especially for severe noise levels, such Minimum MSE (MMSE) solutions may lead to blurry output images. In this work we propose a novel stochastic denoising approach that produces viable and high perceptual quality results, while maintaining a small MSE. Our method employs Langevin dynamics that relies on a repeated application of any given MMSE denoiser, obtaining the reconstructed image by effectively sampling from the posterior distribution. Due to its stochasticity, the proposed algorithm can produce a variety of high-quality outputs for a given noisy input, all shown to be legitimate denoising results. In addition, we present an extension of our algorithm for handling the inpainting problem, recovering missing pixels while removing noise from partially given data.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). Builds on 28 of its 59 references that are in the map. First posted on arXiv 23 Jan 2021.

Builds on

28 of 59 references.

References · 28

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  6. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,580
  7. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  8. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  9. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
  10. 2017Deep Image Priorcited by 1,097
  11. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  12. 2017The Perception-Distortion Tradeoffcited by 582
16 more
  1. 2017FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoisingcited by 509
  2. 2020PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Modelscited by 358
  3. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  4. 2017MemNet: A Persistent Memory Network for Image Restorationcited by 244
  5. 2015Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restorationcited by 194
  6. 2018Residual Dense Network for Image Restorationcited by 181
  7. 2018Non-Local Recurrent Network for Image Restorationcited by 160
  8. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 78
  9. 2018Deep Bayesian Inversioncited by 60
  10. 2019Explorable Super Resolutioncited by 44
  11. 2019Inverting Deep Generative models, One layer at a timecited by 33
  12. 2015A Review Paper: Noise Models in Digital Image Processingcited by 23
  13. 2018Class-Aware Fully-Convolutional Gaussian and Poisson Denoisingcited by 12
  14. 2020Fast Mixing of Multi-Scale Langevin Dynamics under the Manifold Hypothesiscited by 11
  15. 2020When and How Can Deep Generative Models be Inverted?cited by 8
  16. 2018Deep-Energy: Unsupervised Training of Deep Neural Networkscited by 1

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Citing papers per year: 2021: 6; 2022: 13; 2023: 16; 2024: 7; 2025: 3.

45 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2022Denoising Diffusion Restoration Modelscited by 951
  3. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 275
  4. 2021Deblurring via Stochastic Refinementcited by 248
  5. 2022Riemannian Score-Based Generative Modellingcited by 216
  6. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  7. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  8. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  9. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  10. 2021PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Priorcited by 78
  11. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  12. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
33 more
  1. 2022MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusioncited by 66
  2. 2021A Theory of the Distortion-Perception Tradeoff in Wasserstein Spacecited by 52
  3. 2023How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Controlcited by 50
  4. 2022JPEG Artifact Correction using Denoising Diffusion Restoration Modelscited by 45
  5. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  6. 2022Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidancecited by 33
  7. 2023An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systemscited by 33
  8. 2024Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restorationcited by 32
  9. 2023Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problemscited by 28
  10. 2022Threat Model-Agnostic Adversarial Defense using Diffusion Modelscited by 24
  11. 2022Boomerang: Local sampling on image manifolds using diffusion modelscited by 16
  12. 2023Deep Optimal Transport: A Practical Algorithm for Photo-realistic Image Restorationcited by 15
  13. 2023Score Priors Guided Deep Variational Inference for Unsupervised Real-World Single Image Denoisingcited by 15
  14. 2022Conditional Injective Flows for Bayesian Imagingcited by 13
  15. 2022Reasons for the Superiority of Stochastic Estimators over Deterministic Ones: Robustness, Consistency and Perceptual Qualitycited by 13
  16. 2023From Posterior Sampling to Meaningful Diversity in Image Restorationcited by 12
  17. 2023Restoration by Generation with Constrained Priorscited by 9
  18. 2023SVNR: Spatially-variant Noise Removal with Denoising Diffusioncited by 8
  19. 2023Thompson Sampling with Diffusion Generative Priorcited by 7
  20. 2023Product of Gaussian Mixture Diffusion Modelscited by 6
  21. 2024Random Walks with Tweedie: A Unified View of Score-Based Diffusion Modelscited by 6
  22. 2021Posterior Sampling for Image Restoration using Explicit Patch Priorscited by 5
  23. 2022Neural Volume Super-Resolutioncited by 5
  24. 2023Nested Diffusion Processes for Anytime Image Generationcited by 5
  25. 2023Reconstruct-and-Generate Diffusion Model for Detail-Preserving Image Denoisingcited by 5
  26. 2024Dreamguider: Improved Training free Diffusion-based Conditional Generationcited by 4
  27. 2022Complex-valued Retrievals From Noisy Images Using Diffusion Modelscited by 3
  28. 2024Perceptual Fairness in Image Restorationcited by 2
  29. 2025Diffusion^2: Dual Diffusion Model with Uncertainty-Aware Adaptive Noise for Momentary Trajectory Predictioncited by 1
  30. 2023A Scalable Training Strategy for Blind Multi-Distribution Noise Removalcited by 0
  31. 2023Denoising diffusion-based synthetic generation of three-dimensional (3D) anisotropic microstructures from two-dimensional (2D) micrographscited by 0
  32. 2025NnD: Diffusion-based Generation of Physically-Nonnegative Objectscited by 0
  33. 2025Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidancecited by 0