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Fiat-127, a car from the 70s, as imagined by Gemini This chapter covers the mathematical foundations of generative modeling: from mixture models and the EM algorithm to variational autoencoders and diffusion models.

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, amortized inference, and the ELBO derivation.

Diffusion Models

Denoising diffusion and stable diffusion tutorial.