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3D generative modeling is accelerating as the technology allowing the captureof geometric data is developing. However, the acquired data is ofteninconsistent, resulting in unregistered meshes or point clouds. Many generativelearning algorithms require correspondence between each point when comparingthe predicted shape and the target shape. We propose an architecture able tocope with different parameterizations, even during the training phase. Inparticular, our loss function is built upon a kernel-based metric over arepresentation of meshes using geometric measures such as currents andvarifolds. The latter allows to implement an efficient dissimilarity measurewith many desirable properties such as robustness to resampling of the mesh orpoint cloud. We demonstrate the efficiency and resilience of our model with agenerative learning task of human faces.

Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measures