Datar, AdwaitAdwaitDatarAy, NihatNihatAy2025-11-192025-11-192025-107th International Conference on Geometric Science of Information, GSI 2025https://hdl.handle.net/11420/58929We introduce a new version of the KL-divergence for Gaussian distributions which is based on Wasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space {R}^n. In particular, we can evaluate the WKL-divergence of the Dirac measures concentrated in two points which turns out to be proportional to the squared distance between these points.enWasserstein geometryKullback-Leibler divergenceGaussian distributionsOtto metricComputer Science, Information and General Works::005: Computer Programming, Programs, Data and Security::005.7: DataConference Paper10.1007/978-3-032-03921-7_10Conference Paper