  It is nontrivial to store rapidly growing big data nowadays, which demands
high-performance lossless compression techniques. Likelihood-based generative
models have witnessed their success on lossless compression, where flow based
models are desirable in allowing exact data likelihood optimisation with
bijective mappings. However, common continuous flows are in contradiction with
the discreteness of coding schemes, which requires either 1) imposing strict
constraints on flow models that degrades the performance or 2) coding numerous
bijective mapping errors which reduces the efficiency. In this paper, we
investigate volume preserving flows for lossless compression and show that a
bijective mapping without error is possible. We propose Numerical Invertible
Volume Preserving Flow (iVPF) which is derived from the general volume
preserving flows. By introducing novel computation algorithms on flow models,
an exact bijective mapping is achieved without any numerical error. We also
propose a lossless compression algorithm based on iVPF. Experiments on various
datasets show that the algorithm based on iVPF achieves state-of-the-art
compression ratio over lightweight compression algorithms.
