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

Generalization of the Change of Variables Formula with Applications to Residual Flows