mlsanityData to 7 Oct 2026

Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images

arXiv 2106.07009 ↗First posted 13 Jun 2021eess.IV cs.CV cs.LGcited by 110

Not on the map. Why?

Cited by 53 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of log likelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.

Key facts. Cited by 110 papers in the map (data through 7 Oct 2026). Builds on 8 of its 30 references that are in the map. First posted on arXiv 13 Jun 2021.

Builds on

8 of 30 references.

References · 8

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018Noise2Noise: Learning Image Restoration without Clean Datacited by 526
  3. 2018Noise2Void - Learning Denoising from Single Noisy Imagescited by 359
  4. 2019Noise2Self: Blind Denoising by Self-Supervisioncited by 274
  5. 2019High-Quality Self-Supervised Deep Image Denoisingcited by 161
  6. 2019Noisier2Noise: Learning to Denoise from Unpaired Noisy Datacited by 125
  7. 2020Noise2Same: Optimizing A Self-Supervised Bound for Image Denoisingcited by 56
  8. 2020AR-DAE: Towards Unbiased Neural Entropy Gradient Estimationcited by 19

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 12; 2023: 19; 2024: 23; 2025: 33; 2026: 21.

110 papers.

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  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  2. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  3. 2022Diffusion Models for Medical Image Analysis: A Comprehensive Surveycited by 269
  4. 2023Image Restoration with Mean-Reverting Stochastic Differential Equationscited by 182
  5. 2022Diffusion-based Image Translation using Disentangled Style and Content Representationcited by 148
  6. 2023Score-based Data Assimilationcited by 91
  7. 2022MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusioncited by 66
  8. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 60
  9. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistentcited by 58
  10. 2023Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Modelscited by 53
  11. 2023DDM2: Self-Supervised Diffusion MRI Denoising with Generative Diffusion Modelscited by 50
  12. 2023Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Datacited by 40
38 more
  1. 2023Don't Play Favorites: Minority Guidance for Diffusion Modelscited by 37
  2. 2023DiffFashion: Reference-based Fashion Design with Structure-aware Transfer by Diffusion Modelscited by 33
  3. 2023Spatially Adaptive Self-Supervised Learning for Real-World Image Denoisingcited by 33
  4. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Datacited by 32
  5. 2023General Image-to-Image Translation with One-Shot Image Guidancecited by 31
  6. 2022A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noisecited by 29
  7. 2024Transfer CLIP for Generalizable Image Denoisingcited by 29
  8. 2024It's All About Your Sketch: Democratising Sketch Control in Diffusion Modelscited by 28
  9. 2023Controllable Inversion of Black-Box Face Recognition Models via Diffusioncited by 22
  10. 2023MagiCapture: High-Resolution Multi-Concept Portrait Customizationcited by 20
  11. 2025Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulationcited by 19
  12. 2021Noise Distribution Adaptive Self-Supervised Image Denoising using Tweedie Distribution and Score Matchingcited by 18
  13. 2023Unleashing the Power of Self-Supervised Image Denoising: A Comprehensive Reviewcited by 17
  14. 2025Diffusion models for inverse problemscited by 15
  15. 2022Physics-/Model-Based and Data-Driven Methods for Low-Dose Computed Tomography: A surveycited by 14
  16. 2023Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problemscited by 14
  17. 2024TweedieMix: Improving Multi-Concept Fusion for Diffusion-based Image/Video Generationcited by 14
  18. 2025Falcon: Fast Visuomotor Policies via Partial Denoisingcited by 14
  19. 2024Generalized Recorrupted-to-Recorrupted: Self-Supervised Learning Beyond Gaussian Noisecited by 13
  20. 2024Generative AI-Driven Human Digital Twin in IoT-Healthcare: A Comprehensive Surveycited by 11
  21. 2024LDMol: A Text-to-Molecule Diffusion Model with Structurally Informative Latent Space Surpasses AR Modelscited by 11
  22. 2023Using Diffusion Models to Generate Synthetic Labelled Data for Medical Image Segmentationcited by 10
  23. 2024On the Asymptotic Mean Square Error Optimality of Diffusion Modelscited by 10
  24. 2025Model Already Knows the Best Noise: Bayesian Active Noise Selection via Attention in Video Diffusion Modelcited by 10
  25. 2024Solving Inverse Problems via Diffusion Optimal Controlcited by 7
  26. 2025PLADIS: Pushing the Limits of Attention in Diffusion Models at Inference Time by Leveraging Sparsitycited by 7
  27. 2024Amortized Posterior Sampling with Diffusion Prior Distillationcited by 6
  28. 2024Generating Physical Dynamics under Priorscited by 6
  29. 2024Positive2Negative: Breaking the Information-Lossy Barrier in Self-Supervised Single Image Denoisingcited by 6
  30. 2025Self-Supervised Diffusion MRI Denoising via Iterative and Stable Refinementcited by 6
  31. 2025Score-based Self-supervised MRI Denoisingcited by 6
  32. 2022SLiDE: Self-supervised LiDAR De-snowing through Reconstruction Difficultycited by 5
  33. 2022Learning Task-Oriented Flows to Mutually Guide Feature Alignment in Synthesized and Real Video Denoisingcited by 5
  34. 2024Solving General Noisy Inverse Problem via Posterior Sampling: A Policy Gradient Viewpointcited by 5
  35. 2024Enhancing Diffusion-based Point Cloud Generation with Smoothness Constraintcited by 5
  36. 2026Self-Supervised Learning from Noisy and Incomplete Datacited by 5
  37. 2023Unsupervised Image Denoising with Score Functioncited by 4
  38. 2023Proximal nested sampling with data-driven priors for physical scientistscited by 4

50 most cited of 110 All 110 (JSON)