Can a variational auto-encoder (VAE) learn images whose pixels have been generated from a Gaussian distribution (e.g. $N(0, 1)$), i.e. each pixel is a sample from $N(0, 1)$?
My gut feeling says no, because the VAE adds additional noise $\epsilon$ to the original image in the latent space, and if all images and pixels are random from the same distribution it would be impossible do decode/reconstruct into the particular input image. However, VAEs are a bit of a mystery to me internally. Any help would be appreciated!