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Turning Normalizing Flows into Monge Maps with Geodesic Gaussian Preserving Flows. (arXiv:2209.10873v4 [cs.LG] UPDATED)
cs.LG updates on arXiv.org arxiv.org
Normalizing Flows (NF) are powerful likelihood-based generative models that
are able to trade off between expressivity and tractability to model complex
densities. A now well established research avenue leverages optimal transport
(OT) and looks for Monge maps, i.e. models with minimal effort between the
source and target distributions. This paper introduces a method based on
Brenier's polar factorization theorem to transform any trained NF into a more
OT-efficient version without changing the final density. We do so by learning a …
arxiv distribution factorization generative generative models likelihood maps paper polar research theorem trade transport