  Normalizing flows leverage the Change of Variables Formula (CVF) to define
flexible density models. Yet, the requirement of smooth transformations
(diffeomorphisms) in the CVF poses a significant challenge in the construction
of these models. To enlarge the design space of flows, we introduce
$\mathcal{L}$-diffeomorphisms as generalized transformations which may violate
these requirements on zero Lebesgue-measure sets. This relaxation allows e.g.
the use of non-smooth activation functions such as ReLU. Finally, we apply the
obtained results to planar, radial, and contractive residual flows.
