Another category of deep generative model is the Generative Adversarial Network (GAN) (77) which consists of two models: a generator 𝐺(𝒛; 𝜽 𝑔 ), which maps an input noise variable 𝒛 into the data space, and a discriminator 𝐷(𝒙; 𝜽 𝑑 ), which evaluates whether an input 𝒙 comes from real data or from the generator by outputting a probability 0 ≤ 𝐷(𝒙) ≤ 1. Here 𝜽 𝑔 and 𝜽 𝑑 represents the parameters of the generator and the discriminator, respectively. The generator and discriminator models are trained concurrently in an adversarial game until the generator produces samples that cannot be distinguished from real data by the discriminator. Specifically, 𝐷 and 𝐺 are optimized by playing the following minimax game with value function 𝑉(𝐺, 𝐷): Given arbitrary functions 𝐺 and 𝐷, it is theoretically established that a unique solution exists, where 𝐺 completely recovers the original data distribution, and 𝐷(𝒙) is universally equal to 1/2. The applications of GAN are diverse, including image synthesis, style transfer, image-to-image translation, and text-toimage generation, etc.