mlsanityData to 7 Oct 2026

Image Restoration with Mean-Reverting Stochastic Differential Equations

arXiv 2301.11699 ↗First posted 27 Jan 2023cs.LG cs.CVcited by 182

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Cited by 94 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean state with fixed Gaussian noise. Then, by simulating the corresponding reverse-time SDE, we are able to restore the origin of the low-quality image without relying on any task-specific prior knowledge. Crucially, the proposed mean-reverting SDE has a closed-form solution, allowing us to compute the ground truth time-dependent score and learn it with a neural network. Moreover, we propose a maximum likelihood objective to learn an optimal reverse trajectory that stabilizes the training and improves the restoration results. The experiments show that our proposed method achieves highly competitive performance in quantitative comparisons on image deraining, deblurring, and denoising, setting a new state-of-the-art on two deraining datasets. Finally, the general applicability of our approach is further demonstrated via qualitative results on image super-resolution, inpainting, and dehazing. Code is available at https://github.com/Algolzw/image-restoration-sde.

Key facts. Cited by 182 papers in the map (data through 7 Oct 2026). Builds on 50 of its 76 references that are in the map. First posted on arXiv 27 Jan 2023.

Builds on

50 of 76 references.

References · 50

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38 more
  1. 2021SwinIR: Image Restoration Using Swin Transformercited by 1,869
  2. 2021Restormer: Efficient Transformer for High-Resolution Image Restorationcited by 1,618
  3. 2017Enhanced Deep Residual Networks for Single Image Super-Resolutioncited by 1,543
  4. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  5. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
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  7. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
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  11. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  12. 2022Denoising Diffusion Restoration Modelscited by 951
  13. 2021Uformer: A General U-Shaped Transformer for Image Restorationcited by 864
  14. 2021Multi-Stage Progressive Image Restorationcited by 813
  15. 2016Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurringcited by 722
  16. 2022Simple Baselines for Image Restorationcited by 701
  17. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  18. 2017FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoisingcited by 509
  19. 2017Benchmarking Single Image Dehazing and Beyondcited by 445
  20. 2021SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Modelscited by 415
  21. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 407
  22. 2017DeblurGAN: Blind Motion Deblurring Using Conditional Adversarial Networkscited by 366
  23. 2019DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Bettercited by 361
  24. 2016Deep Joint Rain Detection and Removal from a Single Imagecited by 351
  25. 2022MAXIM: Multi-Axis MLP for Image Processingcited by 301
  26. 2019Progressive Image Deraining Networks: A Better and Simpler Baselinecited by 271
  27. 2022Riemannian Score-Based Generative Modellingcited by 216
  28. 2020SRFlow: Learning the Super-Resolution Space with Normalizing Flowcited by 209
  29. 2022Speech Enhancement and Dereverberation with Diffusion-based Generative Modelscited by 195
  30. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  31. 2020Deblurring by Realistic Blurringcited by 187
  32. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  33. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 110
  34. 2022Speech Enhancement with Score-Based Generative Models in the Complex STFT Domaincited by 102
  35. 2019Single Image Deraining: A Comprehensive Benchmark Analysiscited by 84
  36. 2022Deep Constrained Least Squares for Blind Image Super-Resolutioncited by 47
  37. 2022BSRT: Improving Burst Super-Resolution with Swin Transformer and Flow-Guided Deformable Alignmentcited by 32
  38. 2021Noise Distribution Adaptive Self-Supervised Image Denoising using Tweedie Distribution and Score Matchingcited by 18

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 22; 2024: 64; 2025: 60; 2026: 36.

182 papers.

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  1. 2023ResShift: Efficient Diffusion Model for Image Super-resolution by Residual Shiftingcited by 360
  2. 2024Diffusion Model-Based Image Editing: A Surveycited by 212
  3. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  4. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  5. 2023Low-Light Image Enhancement with Wavelet-based Diffusion Modelscited by 126
  6. 2023Diffusion Models for Image Restoration and Enhancement: A Comprehensive Surveycited by 108
  7. 2023Controlling Vision-Language Models for Multi-Task Image Restorationcited by 108
  8. 2023Refusion: Enabling Large-Size Realistic Image Restoration with Latent-Space Diffusion Modelscited by 86
  9. 2024Selective Hourglass Mapping for Universal Image Restoration Based on Diffusion Modelcited by 73
  10. 2024Diffusion Models in Low-Level Vision: A Surveycited by 73
  11. 2024LightenDiffusion: Unsupervised Low-Light Image Enhancement with Latent-Retinex Diffusion Modelscited by 70
  12. 2023Residual Denoising Diffusion Modelscited by 68
38 more
  1. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problemscited by 65
  2. 2024Efficient Diffusion Model for Image Restoration by Residual Shiftingcited by 64
  3. 2024Diffusion Models, Image Super-Resolution And Everything: A Surveycited by 63
  4. 2024DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Modelscited by 60
  5. 2023EDiffSR: An Efficient Diffusion Probabilistic Model for Remote Sensing Image Super-Resolutioncited by 56
  6. 2024Adversarial Diffusion Compression for Real-World Image Super-Resolutioncited by 49
  7. 2023Image Restoration Through Generalized Ornstein-Uhlenbeck Bridgecited by 41
  8. 2023Reference-guided Controllable Inpainting of Neural Radiance Fieldscited by 40
  9. 2024Structure Matters: Tackling the Semantic Discrepancy in Diffusion Models for Image Inpaintingcited by 40
  10. 2024FoundIR: Unleashing Million-scale Training Data to Advance Foundation Models for Image Restorationcited by 37
  11. 2024FourierMamba: Fourier Learning Integration with State Space Models for Image Derainingcited by 32
  12. 2024Entropy-regularized Diffusion Policy with Q-Ensembles for Offline Reinforcement Learningcited by 29
  13. 2024Conditional Image Synthesis with Diffusion Models: A Surveycited by 29
  14. 2024NTIRE 2024 Challenge on Low Light Image Enhancement: Methods and Resultscited by 26
  15. 2025Visual-Instructed Degradation Diffusion for All-in-One Image Restorationcited by 26
  16. 2024Teaching Tailored to Talent: Adverse Weather Restoration via Prompt Pool and Depth-Anything Constraintcited by 24
  17. 2024Score-based Generative Diffusion Models for Social Recommendationscited by 23
  18. 2024OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offscited by 22
  19. 2023The Emergence of Reproducibility and Generalizability in Diffusion Modelscited by 21
  20. 2024Degradation-Aware Residual-Conditioned Optimal Transport for Unified Image Restorationcited by 21
  21. 2023Resfusion: Denoising Diffusion Probabilistic Models for Image Restoration Based on Prior Residual Noisecited by 19
  22. 2024Low-light Image Enhancement via CLIP-Fourier Guided Wavelet Diffusioncited by 19
  23. 2024Conditional sampling within generative diffusion modelscited by 18
  24. 2024LoRA-IR: Taming Low-Rank Experts for Efficient All-in-One Image Restorationcited by 18
  25. 2025UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Controlcited by 18
  26. 2024Beyond Image Super-Resolution for Image Recognition with Task-Driven Perceptual Losscited by 17
  27. 2024Diffusion-Based Point Cloud Super-Resolution for mmWave Radar Datacited by 17
  28. 2023Uncertainty Quantification via Neural Posterior Principal Componentscited by 16
  29. 2024MoE-DiffIR: Task-customized Diffusion Priors for Universal Compressed Image Restorationcited by 15
  30. 2025Consistency Trajectory Matching for One-Step Generative Super-Resolutioncited by 15
  31. 2025Diffusion models for inverse problemscited by 15
  32. 2023Mixed Hierarchy Network for Image Restorationcited by 14
  33. 2024RecDiffusion: Rectangling for Image Stitching with Diffusion Modelscited by 14
  34. 2024Sharing Key Semantics in Transformer Makes Efficient Image Restorationcited by 14
  35. 2024DiffRetouch: Using Diffusion to Retouch on the Shoulder of Expertscited by 14
  36. 2025Residual Diffusion Bridge Model for Image Restorationcited by 14
  37. 2026Learning Continuous Wasserstein Barycenter Space for Generalized All-in-One Image Restorationcited by 14
  38. 2024Implicit Image-to-Image Schrodinger Bridge for Image Restorationcited by 13

50 most cited of 182 All 182 (JSON)