# Noise Distribution Adaptive Self-Supervised Image Denoising using Tweedie Distribution and Score Matching

arXiv: https://arxiv.org/abs/2112.03696 · HTML: https://mlsanity.com/paper/2112.03696/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [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)
- [High-Quality Self-Supervised Deep Image Denoising](https://mlsanity.com/paper/1901.10277/) (2019)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [Noise2Same: Optimizing A Self-Supervised Bound for Image Denoising](https://mlsanity.com/paper/2010.11971/) (2020)
- [AR-DAE: Towards Unbiased Neural Entropy Gradient Estimation](https://mlsanity.com/paper/2006.05164/) (2020)

## Built on by (most cited first, 18 of 18)

- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Spatially Adaptive Self-Supervised Learning for Real-World Image Denoising](https://mlsanity.com/paper/2303.14934/) (2023)
- [Unleashing the Power of Self-Supervised Image Denoising: A Comprehensive Review](https://mlsanity.com/paper/2308.00247/) (2023)
- [NTIRE 2025 Challenge on Efficient Burst HDR and Restoration: Datasets, Methods, and Results](https://mlsanity.com/paper/2505.12089/) (2025)
- [Generalized Recorrupted-to-Recorrupted: Self-Supervised Learning Beyond Gaussian Noise](https://mlsanity.com/paper/2412.04648/) (2024)
- [On the Benefit of Dual-domain Denoising in a Self-supervised Low-dose CT Setting](https://mlsanity.com/paper/2211.01111/) (2022)
- [Positive2Negative: Breaking the Information-Lossy Barrier in Self-Supervised Single Image Denoising](https://mlsanity.com/paper/2412.16460/) (2024)
- [Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2407.02744/) (2024)
- [Self-Supervised Learning from Noisy and Incomplete Data](https://mlsanity.com/paper/2601.03244/) (2026)
- [Noise2Contrast: Multi-Contrast Fusion Enables Self-Supervised Tomographic Image Denoising](https://mlsanity.com/paper/2212.04832/) (2022)
- [Masked Pre-training Enables Universal Zero-shot Denoiser](https://mlsanity.com/paper/2401.14966/) (2024)
- [DiffDenoise: Self-Supervised Medical Image Denoising with Conditional Diffusion Models](https://mlsanity.com/paper/2504.00264/) (2025)
- [SecDiff: Diffusion-Aided Secure Deep Joint Source-Channel Coding Against Adversarial Attacks](https://mlsanity.com/paper/2511.01466/) (2025)
- [Energy-Tweedie: Score meets Score, Energy meets Energy](https://mlsanity.com/paper/2512.23818/) (2025)
- [I2V: Towards Texture-Aware Self-Supervised Blind Denoising using Self-Residual Learning for Real-World Images](https://mlsanity.com/paper/2302.10523/) (2023)
- [UNICORN: Ultrasound Nakagami Imaging via Score Matching and Adaptation](https://mlsanity.com/paper/2403.06275/) (2024)
- [Noise2Score3D:Unsupervised Tweedie's Approach for Point Cloud Denoising](https://mlsanity.com/paper/2502.16826/) (2025)
- [UNICORN: Ultrasound Nakagami Imaging via Score Matching and Adaptation for Assessing Hepatic Steatosis](https://mlsanity.com/paper/2603.16942/) (2026)

## Abstract (arXiv)

Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern deep learning era, leading to a distribution independent self-supervised image denoising formula without clean reference images. Specifically, by combining with the recent Noise2Score self-supervised image denoising approach and the saddle point approximation of Tweedie distribution, we can provide a general closed-form denoising formula that can be used for large classes of noise distributions without ever knowing the underlying noise distribution. Similar to the original Noise2Score, the new approach is composed of two successive steps: score matching using perturbed noisy images, followed by a closed form image denoising formula via distribution-independent Tweedie's formula. This also suggests a systematic algorithm to estimate the noise model and noise parameters for a given noisy image data set. Through extensive experiments, we demonstrate that the proposed method can accurately estimate noise models and parameters, and provide the state-of-the-art self-supervised image denoising performance in the benchmark dataset and real-world dataset.