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In this paper, we advocate the adoption of metric preservation as a powerful prior for learning latent representations of deformable 3D shapes. Key to our construction is the introduction of a geometric distortion criterion, defined directly on the decoded shapes, translating the preservation of the metric on the decoding to the formation of linear paths in the underlying latent space. Our rationale lies in the observation that training samples alone are often insufficient to endow generativearXiv:2003.12283v2 fatcat:bcv2elssh5brhcxtutv52v5fki