If you read the paper https://arxiv.org/abs/1705.09558, in section 2.1, it defines two conditional posteriors for the parameters of the generator and discriminator. Then, classical GAN is just a maximum likelihood estimate (or, a MAP estimate with uniform prior) of the parameters.

Next, the paper said: how about sampling the whole posterior distribution instead of finding only one point of maximum likelihood as classical GANs do. This is the point where the famous Markov chain Monte Carlo (MCMC) algorithms become useful. They use something called stochastic gradient Hamiltonian Monte Carlo, basically, it is a random walk algorithm, at each step, you follow a noisy gradient, as a result, you converge to the posterior distribution instead of a local minima as gradient descent does.

The paper claims that sampling the whole posterior helps to resolve problems with classical GANs. IMHO, this isn't a surprise claim, this is exactly what is good about Bayesian statistics.