Before diffusion, before normalizing flows, before latent diffusion models quietly built VAE encoders into every serious generative stack — there was Kingma and Welling's 2013 paper introducing the variational autoencoder and the reparameterization trick. This revisit goes back to the classic that made stochastic gradient descent through a sampling operation possible in the first place, and shows why the ideas still power modern generative AI from Stable Diffusion to neural speech codecs like EnCodec and SoundStream.

The walkthrough covers the core problem the paper solved: how to do efficient inference and learning in directed probabilistic models with continuous latent variables and intractable posterior distributions, at scale on large datasets. The reparameterization trick is the pivot — expressing the sampled latent as a deterministic function of the parameters plus injected noise, which lets gradients flow through cleanly and unlocks scalable stochastic variational inference. Expect a clean derivation of the ELBO, the recognition-model framing that inspired every modern encoder network, and enough intuition to see why VAEs still show up as the latent-space backbone under so many of today's generative systems. Worth 10 minutes if you want to actually understand what's happening inside the latent.