I am reading about GANs. I understand that GANs learn implicitly the probability distribution that generated the data. However, at the input we give a random noise vector. It seems that we can sample that random noise vector from whatever distribution we want.
My question is: given that there is ONLY ONE possible distribution that could have generated the data, and that our GAN is trying to approximate that distribution, can i think that the GAN also learns how to map between that distribution that it needs to learn and the distribution from which we sample the random noise vector? I am thinking about this, as the random noise vector can be sampled from whatever distribution we want, so it can be different each time we start to train, so it can vary, but the GAN needs to be able to still imitate one unique distribution, so in a way it needs to be able to adapt to the distribution from which the noise comes.