  We marry ideas from deep neural networks and approximate Bayesian inference
to derive a generalised class of deep, directed generative models, endowed with
a new algorithm for scalable inference and learning. Our algorithm introduces a
recognition model to represent approximate posterior distributions, and that
acts as a stochastic encoder of the data. We develop stochastic
back-propagation -- rules for back-propagation through stochastic variables --
and use this to develop an algorithm that allows for joint optimisation of the
parameters of both the generative and recognition model. We demonstrate on
several real-world data sets that the model generates realistic samples,
provides accurate imputations of missing data and is a useful tool for
high-dimensional data visualisation.
