A VAE (Kingma & Welling 2013) learns a structured latent space by maximizing the ELBO = E[log p(x|z)] - β·KL(q(z|x)||p(z)). The KL term regularizes the posterior toward N(0,I). Higher β (β-VAE) encourages disentanglement — latent dimensions correspond to independent factors. Interpolation in latent space produces semantically smooth transitions.