> ## Documentation Index > Fetch the complete documentation index at: https://aegean.ai/llms.txt > Use this file to discover all available pages before exploring further. # Latent Transport Models > Latent variable models, variational inference, diffusion, and flow matching, viewed as ways to transport probability mass between simple and complex distributions. 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. Latent variable models, probabilistic graphical models, and the generative modeling framework. Expectation-maximization for maximum likelihood estimation in latent variable models. EM applied to mixture of Gaussians for density estimation and clustering. Variational inference, calculus of variations, and the deep latent variable modeling problem. Encoder-decoder architecture and amortized variational inference. Derivation of the Evidence Lower Bound and joint training of the encoder and decoder. *** [Edit this page on GitHub](https://github.com/aegean-ai/eaia/edit/main/src/book/latent-transport-models/index.mdx) or [file an issue](https://github.com/aegean-ai/eaia/issues/new/choose).