Apologies if it’s too trivial.

Consider paired training data (x,y) where x is edge-image and y is realistic image.

Pix2Pix discriminator training is totally paired i.e. for a given x, y forms the real image and fake_y=G(x) forms the fake image. Note that this is deviating from Conditional GAN paper where for a single label of MNIST say 4, we have a distribution of real images available.

Also, note that the discriminator is pix2pix is conditional on x i.e. D(x,y) and D(x,fake_y) are to be discriminated. So, in principle pix2pix can learn a 1-1 mapping from edges to corresponding shoes in training set and I see no reason why it must produce a variation of shoes as shown in paper.

Assuming this code is correct implementation: https://github.com/junyanz/pytorch-CycleGAN-and-pix2pix/blob/master/models/pix2pix_model.py