I don't understand the images associated with that article. They purport to show the progressive refinement of the output over a series of days. But the figure changes dramatically from image to image, all the way to the end of the run. At the very least it seems the output is not stable: a human has to decide when to stop the Wheel of Fortune. It looks more like a series of images taken from different training sets…
What they are probably doing is showing snapshots of the same noise vector (==random seed) for various epoches. Since the mapping of noise vector ~> face is totally arbitrary, the ProGAN is free to vary it as it pleases; thus, some but not perfect stability. I saw the same thing in messing around with anime GANs: a fixed set of noise vectors would show the anime faces change eye or hair color etc.
> At the very least it seems the output is not stable: a human has to decide when to stop the Wheel of Fortune.
Yeah, you can't do principled early stopping with GANs, really, because there's no held-out set and the loss is changing. I always ran until it diverged or I became impatient, and similarly with ProGAN: they ran as long as they could (takes like a week on big GPUs). To some extent, if you're using Wasserstein losses, the discriminator loss is supposed to be meaningful as a kind of absolute distance between the true image distribution and the generator distribution so you can do early stopping like 'stop if no improvement for 3 epochs'. (This is just in the pure generative approach; if you're using GANs for a semi-supervised application, presumably you can do early stopping as usual based on whatever you have held-out.)