Variational autoencoder

A variational autoencoder (VAE) is a deep generative model that learns a compressed latent representation of data by optimizing a variational lower bound on the data likelihood. It consists of an encoder network that approximates the posterior over latent variables given observations, and a decoder network that reconstructs observations from latents. The training objective — the evidence lower bound (ELBO) — balances reconstruction fidelity against the KL divergence between the approximate posterior and a prior, typically a standard Gaussian. By forcing latent representations to match a simple prior, the VAE learns a structured, continuous latent space in which interpolation between data points produces semantically meaningful intermediate states. The VAE is the point where variational inference meets deep learning, and its architecture has spawned descendants ranging from beta-VAE (which disentangles latent factors) to hierarchical VAEs that stack latent variables at multiple scales.