  As a probabilistic modeling technique, the flow-based model has demonstrated
remarkable potential in the field of lossless compression
\cite{idf,idf++,lbb,ivpf,iflow},. Compared with other deep generative models
(eg. Autoregressive, VAEs) \cite{bitswap,hilloc,pixelcnn++,pixelsnail} that
explicitly model the data distribution probabilities, flow-based models perform
better due to their excellent probability density estimation and satisfactory
inference speed. In flow-based models, multi-scale architecture provides a
shortcut from the shallow layer to the output layer, which significantly
reduces the computational complexity and avoid performance degradation when
adding more layers. This is essential for constructing an advanced flow-based
learnable bijective mapping. Furthermore, the lightweight requirement of the
model design in practical compression tasks suggests that flows with
multi-scale architecture achieve the best trade-off between coding complexity
and compression efficiency.
