# On the exact relationship between the denoising function and the data distribution

arXiv: https://arxiv.org/abs/1709.02797 · HTML: https://mlsanity.com/paper/1709.02797/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2017.

## Built on by (most cited first, 1 of 1)

- [SAFARI: Safe and Active Robot Imitation Learning with Imagination](https://mlsanity.com/paper/2011.09586/) (2020)

## Abstract (arXiv)

We prove an exact relationship between the optimal denoising function and the data distribution in the case of additive Gaussian noise, showing that denoising implicitly models the structure of data allowing it to be exploited in the unsupervised learning of representations. This result generalizes a known relationship [2], which is valid only in the limit of small corruption noise.