  Deep latent variable models have seen recent success in many data domains.
Lossless compression is an application of these models which, despite having
the potential to be highly useful, has yet to be implemented in a practical
manner. We present `Bits Back with ANS' (BB-ANS), a scheme to perform lossless
compression with latent variable models at a near optimal rate. We demonstrate
this scheme by using it to compress the MNIST dataset with a variational
auto-encoder model (VAE), achieving compression rates superior to standard
methods with only a simple VAE. Given that the scheme is highly amenable to
parallelization, we conclude that with a sufficiently high quality generative
model this scheme could be used to achieve substantial improvements in
compression rate with acceptable running time. We make our implementation
available open source at https://github.com/bits-back/bits-back .
