# Learning by Denoising Part 2. Connection between data distribution and denoising function

In this blog post, we complement our first post and examine denoising from a more analytic perspective with detailed mathematical derivations. We will show that there is a unique two-way connection between the uncorrupted data distribution \(p(x)\) and the optimal denoising function \(g(\tilde x)\), provided that the corruption noise is Gaussian. The corrupted distribution \(p(\tilde x)\) plays a central role (more…)