(coauthor here) We used an adversarial loss in addition to a perceptual loss and MSE. None of these work super-well when the others are not used.
The adversarial loss "learns" what is a compressed image and tries to make the decoder go away from such outputs.
The perceptual (LPIPS) is not so sensitive to pure noise and allows for it, but is sensitive to texture details.
MSE tries to get the rough shape right.
We also asked users in a study to tell us which images they preferred when having access to the original. Most prefer the added details even if they're not exactly right.