# Generalized Recorrupted-to-Recorrupted: Self-Supervised Learning Beyond Gaussian Noise

arXiv: https://arxiv.org/abs/2412.04648 · HTML: https://mlsanity.com/paper/2412.04648/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 5 Dec 2024.

## Builds on (most cited first, 20 of 20)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [Measuring Forgetting of Memorized Training Examples](https://mlsanity.com/paper/2207.00099/) (2022)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Blind2Unblind: Self-Supervised Image Denoising with Visible Blind Spots](https://mlsanity.com/paper/2203.06967/) (2022)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Unsupervised Learning From Incomplete Measurements for Inverse Problems](https://mlsanity.com/paper/2201.12151/) (2022)
- [Noise Distribution Adaptive Self-Supervised Image Denoising using Tweedie Distribution and Score Matching](https://mlsanity.com/paper/2112.03696/) (2021)
- [SAR Image Despeckling by Deep Neural Networks: from a pre-trained model to an end-to-end training strategy](https://mlsanity.com/paper/2006.15559/) (2020)
- [Unbiased Risk Estimation in the Normal Means Problem via Coupled Bootstrap Techniques](https://mlsanity.com/paper/2111.09447/) (2021)
- [Audio Texture Synthesis with Scattering Moments](https://mlsanity.com/paper/1311.0407/) (2013)
- [Image Denoising and the Generative Accumulation of Photons](https://mlsanity.com/paper/2307.06607/) (2023)
- [Unbiased Test Error Estimation in the Poisson Means Problem via Coupled Bootstrap Techniques](https://mlsanity.com/paper/2212.01943/) (2022)

## Built on by (most cited first, 13 of 13)

- [Self-Supervised Learning from Noisy and Incomplete Data](https://mlsanity.com/paper/2601.03244/) (2026)
- [Normalization-equivariant Diffusion Models: Learning Posterior Samplers From Noisy And Partial Measurements](https://mlsanity.com/paper/2510.11964/) (2025)
- [Reconstruct Anything Model: a lightweight general model for computational imaging](https://mlsanity.com/paper/2503.08915/) (2025)
- [Equivariant Splitting: Self-supervised learning from incomplete data](https://mlsanity.com/paper/2510.00929/) (2025)
- [See the past: Time-Reversed Scene Reconstruction from Thermal Traces Using Visual Language Models](https://mlsanity.com/paper/2510.05408/) (2025)
- [Learning to Recorrupt: Noise Distribution Agnostic Self-Supervised Image Denoising](https://mlsanity.com/paper/2603.25869/) (2026)
- [Hypothesis Testing in Imaging Inverse Problems](https://mlsanity.com/paper/2505.22481/) (2025)
- [SDPA++: A General Framework for Self-Supervised Denoising with Patch Aggregation](https://mlsanity.com/paper/2510.16702/) (2025)
- [Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements](https://mlsanity.com/paper/2510.27663/) (2025)
- [Scale Equivariance Regularization and Feature Lifting in High Dynamic Range Modulo Imaging](https://mlsanity.com/paper/2601.23037/) (2026)
- [Perspective-Equivariant Fine-tuning for Multispectral Demosaicing without Ground Truth](https://mlsanity.com/paper/2603.01332/) (2026)
- [Physen-Noise2Noise: Physics-Guided Self-Supervised Defocus Deblurring with Bias Correction under Low-Light Conditions](https://mlsanity.com/paper/2605.24590/) (2026)
- [Frozen CLIP Priors for Robust Self-Supervised Poisson Inverse Problems](https://mlsanity.com/paper/2608.20524/) (2026)

## Abstract (arXiv)

Recorrupted-to-Recorrupted (R2R) has emerged as a methodology for training deep networks for image restoration in a self-supervised manner from noisy measurement data alone, demonstrating equivalence in expectation to the supervised squared loss in the case of Gaussian noise. However, its effectiveness with non-Gaussian noise remains unexplored. In this paper, we propose Generalized R2R (GR2R), extending the R2R framework to handle a broader class of noise distribution as additive noise like log-Rayleigh and address the natural exponential family including Poisson and Gamma noise distributions, which play a key role in many applications including low-photon imaging and synthetic aperture radar. We show that the GR2R loss is an unbiased estimator of the supervised loss and that the popular Stein's unbiased risk estimator can be seen as a special case. A series of experiments with Gaussian, Poisson, and Gamma noise validate GR2R's performance, showing its effectiveness compared to other self-supervised methods.