  Flow-based generative models are an important class of exact inference models
that admit efficient inference and sampling for image synthesis. Owing to the
efficiency constraints on the design of the flow layers, e.g. split coupling
flow layers in which approximately half the pixels do not undergo further
transformations, they have limited expressiveness for modeling long-range data
dependencies compared to autoregressive models that rely on conditional
pixel-wise generation. In this work, we improve the representational power of
flow-based models by introducing channel-wise dependencies in their latent
space through multi-scale autoregressive priors (mAR). Our mAR prior for models
with split coupling flow layers (mAR-SCF) can better capture dependencies in
complex multimodal data. The resulting model achieves state-of-the-art density
estimation results on MNIST, CIFAR-10, and ImageNet. Furthermore, we show that
mAR-SCF allows for improved image generation quality, with gains in FID and
Inception scores compared to state-of-the-art flow-based models.
