I understand the general notion of likelihood as "probability to generate the data given parameters" (like here). But people use (log-)likelihood as a measure of "goodness" of a generative model.
But, e.g., let's take a look at Generative Adversarial Networks model. It takes some random noise and deterministically (using a neural network) transforms it to a sample. If we take a look at a particular (test) sample with a couple of thousands of pixels, isn't the probability that it will be generated 0? As it is very improbable to get the exact values of each pixel in each place and could possibly happen to at most one setting of "noise" anyway?
How is the likelihood defined in terms of GANs and other generative models?