Variational Autoencoders

Variational autoencoders learn probability distributions over compact latent codes and decode samples from them, typically by balancing reconstruction quality against a KL-divergence regularizer in the evidence lower bound. Common approaches use Gaussian, mixture, flow-based, spherical, or heavy-tailed priors, and add hierarchical, disentangling, temporal, multimodal, geometric, or physics-informed structure. They are used for image, video, audio, molecule, medical, and scientific data, both as generative models and as compact representations for downstream prediction or diffusion. A central tension is that stronger regularization can make generation easier while causing posterior collapse or losing useful detail; reconstruction scores alone also do not guarantee good samples, calibrated uncertainty, or useful latent structure.