  Recent work has shown that Neural Ordinary Differential Equations (ODEs) can
serve as generative models of images using the perspective of Continuous
Normalizing Flows (CNFs). Such models offer exact likelihood calculation, and
invertible generation/density estimation. In this work we introduce a
Multi-Resolution variant of such models (MRCNF), by characterizing the
conditional distribution over the additional information required to generate a
fine image that is consistent with the coarse image. We introduce a
transformation between resolutions that allows for no change in the log
likelihood. We show that this approach yields comparable likelihood values for
various image datasets, with improved performance at higher resolutions, with
fewer parameters, using only 1 GPU. Further, we examine the out-of-distribution
properties of (Multi-Resolution) Continuous Normalizing Flows, and find that
they are similar to those of other likelihood-based generative models.
