When doing auto encoders on images L1 loss is the standard choice but it tend to produce blurry images. Is there any literature that have a learnable loss, maybe something like GANs or some other function that takes a target image and an output from the network but is also trainable?

I haven’t seen this in the VAE and AE papers I’ve read but I’m sure there are lots of examples. Have you found any learnable losses or similar approaches?