The title of the question is basically all I'm asking, but I should explain why GANs don't seem to be unsupervised to me!
Here's my understanding of unsupervised learning: Unsupervised learning is when you have an set of data (the X values) but no classes (y values). It's typically done for clustering similar samples in the data together.
Here's my understanding of how a GAN works: You have a generator that produces a sample of the data from a random noise input. Many hundreds of samples are generated and fed to the discriminator along with a bunch of real examples; the discriminator processes each sample and outputs the likelihood that each sample is real or generated. The discriminators predictions are compared to the true (whether or not the sample was generated) and then discriminator goes through a back propagation cycle to learn to discriminate better. The predictions from the discriminator are also fed back to the generator as cost (or I guess 1-cost if the discriminator using 1 to represent real, and 0 to represent fake). The generator then goes through back propagation to get better at fooling the discriminator.
If both of the statements above are true, the system can't work without labelled data and hence is supervised learning. The problem is I've read multiple articles that flat out state that generative adversarial networks are unsupervised. Where am I hitting my head against the wall?