Conditional GAN

Definition

Conditional GAN (cGAN) is an extension of GAN that allows for the generating of data with specific attributes or conditions. In a standard GAN, the generator only takes random noise, while in a cGAN, the generator receives additional information to guide the generation process.

Architecture

The generator learns to create samples that match the given condition, and the discriminator learns to distinguish between real and fake samples, considering the condition.

Objective Function

The objective function of cGAN is defined as ${\min }_{{\theta }_G}{\max }_{{\theta }_D}[E_{x\sim p_r(x)}[\ln D(x|c)]+E_{z\sim p(z)}[\ln (1-D(G(z|c)))]]$ where:

• $G(z|c)$ is the generator’s output given noise and condition
• $D(x|c)$ is the discriminator’s output given input and condition
• $c$ is the condition
• $p_r$ is the distribution of the input data
• $p_z$ is the distribution of noise