The algorithm itself tries to learn to remove noise. This part of algorithm is undeniably a learning process, evidenced by the fact that it gets better along the training process. It just happens to be that, in order to remove noise, you need to have an understanding of the underlying thing(probability distribution), so in order to learn to remove noise, it needs to learn the images. I don't understand how a mathematical function by definition can't learn, since it's just a language we use to describe what's going on.