I understand that you want to know about methods that we can use to evaluate GANs (Generative Adversarial Networks).
How can GANs be evaluated?
One Discriminator on Separate GANs
We can train a Discriminator beforehand and then we can use this Discriminator on various Generators to see what does this Discriminator say about the images generated from each Generator. The average output of the Discriminator for images generated from one Generator can be compared with that of the images generated from another Generator. This means that according to this Discriminator, one Generator is better than another.
Comparing Probabilistic Models
This is the class of evaluation metrics that is attracting research attention recently. Basically, all generative models are probabilistic in nature, even GANs. When we ask a generative model to generate something like an image, we are simply sampling from a probability distribution. This means that if we can compare the probability distributions of our Generator and that of our original data then we will have an evaluation metric. We can come up with a kernel function to define these probability distributions more accurately. Then we can take our generated samples from the Generator and see the probability of that sample being taken from the original distribution. Researchers have also utilized KL-divergence for comparing samples generated from two distributions.
Note: KL-divergence can not be directly applied in this case because corresponding ground truth is not available. However, there are some modifications proposed in the research work mentioned.