  Normalizing flows have received a great deal of recent attention as they
allow flexible generative modeling as well as easy likelihood computation.
While a wide variety of flow models have been proposed, there is little formal
understanding of the representation power of these models. In this work, we
study some basic normalizing flows and rigorously establish bounds on their
expressive power. Our results indicate that while these flows are highly
expressive in one dimension, in higher dimensions their representation power
may be limited, especially when the flows have moderate depth.
