# Noise2Same: Optimizing A Self-Supervised Bound for Image Denoising

arXiv: https://arxiv.org/abs/2010.11971 · HTML: https://mlsanity.com/paper/2010.11971/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 30 of 56)

- [A Survey on Self-supervised Learning: Algorithms, Applications, and Future Trends](https://mlsanity.com/paper/2301.05712/) (2023)
- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [AP-BSN: Self-Supervised Denoising for Real-World Images via Asymmetric PD and Blind-Spot Network](https://mlsanity.com/paper/2203.11799/) (2022)
- [Random Sub-Samples Generation for Self-Supervised Real Image Denoising](https://mlsanity.com/paper/2307.16825/) (2023)
- [A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noise](https://mlsanity.com/paper/2205.10278/) (2022)
- [Interpretable Unsupervised Diversity Denoising and Artefact Removal](https://mlsanity.com/paper/2104.01374/) (2021)
- [Optimal Transport for Unsupervised Denoising Learning](https://mlsanity.com/paper/2108.02574/) (2021)
- [Self-Supervised Representation Learning via Latent Graph Prediction](https://mlsanity.com/paper/2202.08333/) (2022)
- [Denoising Masked AutoEncoders Help Robust Classification](https://mlsanity.com/paper/2210.06983/) (2022)
- [As if by magic: self-supervised training of deep despeckling networks with MERLIN](https://mlsanity.com/paper/2110.13148/) (2021)
- [Noise Distribution Adaptive Self-Supervised Image Denoising using Tweedie Distribution and Score Matching](https://mlsanity.com/paper/2112.03696/) (2021)
- [Unsupervised Deep Learning Methods for Biological Image Reconstruction and Enhancement](https://mlsanity.com/paper/2105.08040/) (2021)
- [Unleashing the Power of Self-Supervised Image Denoising: A Comprehensive Review](https://mlsanity.com/paper/2308.00247/) (2023)
- [Adaptive Denoising via GainTuning](https://mlsanity.com/paper/2107.12815/) (2021)
- [PUCA: Patch-Unshuffle and Channel Attention for Enhanced Self-Supervised Image Denoising](https://mlsanity.com/paper/2310.10088/) (2023)
- [Self-supervised Learning for Sonar Image Classification](https://mlsanity.com/paper/2204.09323/) (2022)
- [RCRN: Real-world Character Image Restoration Network via Skeleton Extraction](https://mlsanity.com/paper/2207.07795/) (2022)
- [Self-supervised Image Denoising with Downsampled Invariance Loss and Conditional Blind-Spot Network](https://mlsanity.com/paper/2304.09507/) (2023)
- [Masked and Shuffled Blind Spot Denoising for Real-World Images](https://mlsanity.com/paper/2404.09389/) (2024)
- [Score-based Self-supervised MRI Denoising](https://mlsanity.com/paper/2505.05631/) (2025)
- [Self-Supervised Diffusion MRI Denoising via Iterative and Stable Refinement](https://mlsanity.com/paper/2501.13514/) (2025)
- [stMCDI: Masked Conditional Diffusion Model with Graph Neural Network for Spatial Transcriptomics Data Imputation](https://mlsanity.com/paper/2403.10863/) (2024)
- [Asymmetric Mask Scheme for Self-Supervised Real Image Denoising](https://mlsanity.com/paper/2407.06514/) (2024)
- [Positive2Negative: Breaking the Information-Lossy Barrier in Self-Supervised Single Image Denoising](https://mlsanity.com/paper/2412.16460/) (2024)
- [Group Contrastive Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2107.09787/) (2021)
- [Learning Task-Oriented Flows to Mutually Guide Feature Alignment in Synthesized and Real Video Denoising](https://mlsanity.com/paper/2208.11803/) (2022)
- [Patch-Craft Self-Supervised Training for Correlated Image Denoising](https://mlsanity.com/paper/2211.09919/) (2022)
- [GeoTMI:Predicting quantum chemical property with easy-to-obtain geometry via positional denoising](https://mlsanity.com/paper/2304.03724/) (2023)
- [Token Boosting for Robust Self-Supervised Visual Transformer Pre-training](https://mlsanity.com/paper/2304.04175/) (2023)

## Abstract (arXiv)

Self-supervised frameworks that learn denoising models with merely individual noisy images have shown strong capability and promising performance in various image denoising tasks. Existing self-supervised denoising frameworks are mostly built upon the same theoretical foundation, where the denoising models are required to be J-invariant. However, our analyses indicate that the current theory and the J-invariance may lead to denoising models with reduced performance. In this work, we introduce Noise2Same, a novel self-supervised denoising framework. In Noise2Same, a new self-supervised loss is proposed by deriving a self-supervised upper bound of the typical supervised loss. In particular, Noise2Same requires neither J-invariance nor extra information about the noise model and can be used in a wider range of denoising applications. We analyze our proposed Noise2Same both theoretically and experimentally. The experimental results show that our Noise2Same remarkably outperforms previous self-supervised denoising methods in terms of denoising performance and training efficiency. Our code is available at https://github.com/divelab/Noise2Same.