  Likelihood-based generative models are the backbones of lossless compression
due to the guaranteed existence of codes with lengths close to negative log
likelihood. However, there is no guaranteed existence of computationally
efficient codes that achieve these lengths, and coding algorithms must be
hand-tailored to specific types of generative models to ensure computational
efficiency. Such coding algorithms are known for autoregressive models and
variational autoencoders, but not for general types of flow models. To fill in
this gap, we introduce local bits-back coding, a new compression technique for
flow models. We present efficient algorithms that instantiate our technique for
many popular types of flows, and we demonstrate that our algorithms closely
achieve theoretical codelengths for state-of-the-art flow models on
high-dimensional data.
