  In just three years, Variational Autoencoders (VAEs) have emerged as one of
the most popular approaches to unsupervised learning of complicated
distributions. VAEs are appealing because they are built on top of standard
function approximators (neural networks), and can be trained with stochastic
gradient descent. VAEs have already shown promise in generating many kinds of
complicated data, including handwritten digits, faces, house numbers, CIFAR
images, physical models of scenes, segmentation, and predicting the future from
static images. This tutorial introduces the intuitions behind VAEs, explains
the mathematics behind them, and describes some empirical behavior. No prior
knowledge of variational Bayesian methods is assumed.
