  Normalizing flows are a class of probabilistic generative models which allow
for both fast density computation and efficient sampling and are effective at
modelling complex distributions like images. A drawback among current methods
is their significant training cost, sometimes requiring months of GPU training
time to achieve state-of-the-art results. This paper introduces Wavelet Flow, a
multi-scale, normalizing flow architecture based on wavelets. A Wavelet Flow
has an explicit representation of signal scale that inherently includes models
of lower resolution signals and conditional generation of higher resolution
signals, i.e., super resolution. A major advantage of Wavelet Flow is the
ability to construct generative models for high resolution data (e.g., 1024 x
1024 images) that are impractical with previous models. Furthermore, Wavelet
Flow is competitive with previous normalizing flows in terms of bits per
dimension on standard (low resolution) benchmarks while being up to 15x faster
to train.
