Generative Models

A classifier learns p(y | x). A generative model learns p(x) itself, well enough to draw new samples from it. The four families here make different trades between sample quality, speed and an exact likelihood.

A VAE learns an encoder and a decoder, trained with the ELBO, and the reparameterisation trick makes the sampling step differentiable. A GAN drops the likelihood and trains a generator against a discriminator, which gives sharp samples and unstable training. A normalising flow gives an exact likelihood through the change of variables formula, at the cost of invertible layers.

Diffusion models are the current state of the art for images. They learn to remove noise one small step at a time, and the forward process has a closed form, so training is simple and stable.