Datar, AdwaitAdwaitDatarAy, NihatNihatAy2025-08-052025-08-052025-03-31arXiv:2503.24022 (2025)https://hdl.handle.net/11420/56919We introduce a new version of the KL-divergence for Gaussian distributions which is based onWasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space Rn. In particular, we can evaluate the WKLdivergence of the Dirac measures concentrated in two points which turns out to be proportional to the squared distance between these points.enhttps://creativecommons.org/licenses/by/4.0/Technology::600: TechnologyPreprinthttps://doi.org/10.15480/882.15752https://arxiv.org/pdf/2503.2402210.15480/882.157522503.24022v1Preprint