  We introduce the Probabilistic Generative Adversarial Network (PGAN), a new
GAN variant based on a new kind of objective function. The central idea is to
integrate a probabilistic model (a Gaussian Mixture Model, in our case) into
the GAN framework which supports a new kind of loss function (based on
likelihood rather than classification loss), and at the same time gives a
meaningful measure of the quality of the outputs generated by the network.
Experiments with MNIST show that the model learns to generate realistic images,
and at the same time computes likelihoods that are correlated with the quality
of the generated images. We show that PGAN is better able to cope with
instability problems that are usually observed in the GAN training procedure.
We investigate this from three aspects: the probability landscape of the
discriminator, gradients of the generator, and the perfect discriminator
problem.
