  The latent space of normalizing flows must be of the same dimensionality as
their output space. This constraint presents a problem if we want to learn
low-dimensional, semantically meaningful representations. Recent work has
provided compact representations by fitting flows constrained to manifolds, but
hasn't defined a density off that manifold. In this work we consider flows with
full support in data space, but with ordered latent variables. Like in PCA, the
leading latent dimensions define a sequence of manifolds that lie close to the
data. We note a trade-off between the flow likelihood and the quality of the
ordering, depending on the parameterization of the flow.
