Many recent generative models leverage alternative generative frameworks, and among them generative adversarial networks (GANs) are one of the most popular.

The basic idea behind a general GAN-based generative models is: first define a trainable network $g_{\theta}: R^{d}\rightarrow \chi$. This generator network is trained to generate realistic data samples $\tilde{x} \in \chi$ by taking a random seed $z \in R^{d}$ as input.

At the same time, define a discriminator network $d_{\phi}: \chi \rightarrow [0,1]$. The goal of it is to distinguish between real data samples $x \in \chi$ and samples generated by the generator $\tilde{x} \in \chi$.