# One Size Fits All: Can We Train One Denoiser for All Noise Levels?

arXiv: https://arxiv.org/abs/2005.09627 · HTML: https://mlsanity.com/paper/2005.09627/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2020.

## Built on by (most cited first, 10 of 10)

- [Variational Deep Image Restoration](https://mlsanity.com/paper/2207.01074/) (2022)
- [Blind denoising diffusion models and the blessings of dimensionality](https://mlsanity.com/paper/2602.09639/) (2026)
- [The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning](https://mlsanity.com/paper/2602.18428/) (2026)
- [Uncertainty-aware Generalized Adaptive CycleGAN](https://mlsanity.com/paper/2102.11747/) (2021)
- [Noise2Recon: Enabling Joint MRI Reconstruction and Denoising with Semi-Supervised and Self-Supervised Learning](https://mlsanity.com/paper/2110.00075/) (2021)
- [Pivotal Auto-Encoder via Self-Normalizing ReLU](https://mlsanity.com/paper/2406.16052/) (2024)
- [Heteroscedasticity of Denoising Score Matching with Generalised Smooth Noise](https://mlsanity.com/paper/2508.01597/) (2025)
- [Variational Deep Image Denoising](https://mlsanity.com/paper/2104.00965/) (2021)
- [A Scalable Training Strategy for Blind Multi-Distribution Noise Removal](https://mlsanity.com/paper/2310.20064/) (2023)
- [A statistical theory for blind denoising: minimax estimation of the noise level from a single sample](https://mlsanity.com/paper/2609.33008/) (2026)

## Abstract (arXiv)

When training an estimator such as a neural network for tasks like image denoising, it is often preferred to train one estimator and apply it to all noise levels. The de facto training protocol to achieve this goal is to train the estimator with noisy samples whose noise levels are uniformly distributed across the range of interest. However, why should we allocate the samples uniformly? Can we have more training samples that are less noisy, and fewer samples that are more noisy? What is the optimal distribution? How do we obtain such a distribution? The goal of this paper is to address this training sample distribution problem from a minimax risk optimization perspective. We derive a dual ascent algorithm to determine the optimal sampling distribution of which the convergence is guaranteed as long as the set of admissible estimators is closed and convex. For estimators with non-convex admissible sets such as deep neural networks, our dual formulation converges to a solution of the convex relaxation. We discuss how the algorithm can be implemented in practice. We evaluate the algorithm on linear estimators and deep networks.