The Variational Autoencoder (VAE) is a probabilistic variant of auto-encoder 14 proposed by Kingma et al. Instead of encoding inputs into a point estimate (degenerate distribution), the VAE encodes inputs into a conditional probability distribution to form a latent information bottleneck. This approach to latent space design enforces representational continuity and a generative interpretation. By feed-forward propagation, the model may be decomposed into three parts (Figure ). An encoder network approximates a posterior distribution over latent variable z conditioned on input data x, q ϕ (z|x). This effectively distinguishes latent space regions by observation probability as a function of the conditioned data x. The second is an uninformative prior, p(z), usually the standard multivariate Gaussian distribution. The third is a decoder that outputs a likelihood distribution over the data conditioned on the posterior-sampled latent variable z, p θ (x|z), effectively generating a reconstruction of the input on sampling. The training jointly optimizes for encoder and decoder parameters ϕ and θ by maximizing the (evidence) lower bound (ELBO) on the log-likelihood of the data distribution.