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Fiat-127, a car from the 70s, as imagined by Gemini This chapter covers the family of models that move probability mass between a simple latent distribution and a complex data distribution. You start with classical mixture models and the EM algorithm, then deep latent variable models trained with variational inference (VAEs), and finally probability-transport methods that learn continuous trajectories between noise and data: diffusion models and flow matching.

Generative Models & PGMs

Latent variable models, probabilistic graphical models, and the generative modeling framework.

EM Algorithm

Expectation-maximization for maximum likelihood estimation in latent variable models.

Gaussian Mixtures

EM applied to mixture of Gaussians for density estimation and clustering.

VAE Introduction

Variational inference, calculus of variations, and the deep latent variable modeling problem.

VAE Architecture

Encoder-decoder architecture and amortized variational inference.

VAE Optimization

Derivation of the Evidence Lower Bound and joint training of the encoder and decoder.
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