Etymology of "Normalizing Flows"

In the "Learn the basics" tutorial, the etymology of the term "normalizing" in "normalizing" flows is explained as: "normalizing refers to the fact that the base distribution is often a (standard) normal distribution. https://github.com/probabilists/zuko/blob/master/docs/tutorials/basics.ipynb However in the prototypical(?) paper "Variational Inference with Normalizing Flows" it is explained that "By repeatedly applying the rule for change of variables, the initial density ‘flows’ through the sequence of invertible mappings. At the end of this sequence we obtain a valid probability distribution and hence this type of flow is referred to as a normalizing flow." https://arxiv.org/abs/1505.05770 Is the etymology of the term "normalizing" in "normalizing" flows then more accurately explained as derived from the ability of the method to produce a "normalized" valid probability distribution instead of being derived from common use of "normal" distributions in the method?