Generative Adversarial Network

A GAN trains two neural networks against each other:

• The generator takes random noise and turns it into a sample, such as an image.
• The discriminator looks at an image and guesses: real (from the dataset) or fake (from the generator)?

They train in turns. The discriminator learns from its mistakes to spot fakes better. The generator is updated, through the discriminator, to produce images the discriminator would call real. Neither network ever sees a “correct” image to copy; the generator learns purely from the discriminator’s feedback.

When it works, the result is striking: GANs produced the first truly photorealistic synthetic faces. When it doesn’t, the two networks oscillate, or the generator finds one image that fools the discriminator and produces nothing else (mode collapse).

Since about 2021, diffusion models have taken over most image generation because they train more reliably and cover more variety, though GAN ideas live on in fast generators and upscalers.

The math

$$\min_G \max_D \; \mathbb{E}_{x \sim p_\text{data}}[\log D(x)] + \mathbb{E}_{z \sim p(z)}[\log(1 - D(G(z)))]$$