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Generative models, which map a latent parameter space to instances in an ambient space, enjoy various applications in 3D Vision and related domains. A standard scheme of these models is probabilistic, which aligns the induced ambient distribution of a generative model from a prior distribution of the latent space with the empirical ambient distribution of training instances. While this paradigm has proven to be quite successful on images, its current applications in 3D generation encounter fundamental challenges in the limited training data and generalization behavior. The key difference between image generation and shape generation is that 3D shapes possess various priors in geometry, topology, and physical properties. Existing probabilistic 3D generative approaches do not preserve these desired properties, resulting in synthesized shapes with various types of distortions. In this talk, I will discuss recent work that seeks to establish a novel geometric framework for learning shape generators. The key idea is to model various geometric, physical, and topological priors of 3D shapes as suitable regularization losses by developing computational tools in differential geometry and computational topology. We will discuss the applications in deformable shape generation, latent space design, joint shape matching, and 3D man-made shape generation. The papers I will cover in this talk include CoFie (NeurIPS 24), TutteNet (CVPR 24), ARAPReg (ICCV 21), GeoLatent (SIGA23), GenCorres (ICLR24), PDGen (ICML 24), and GPLD3D (CVPR 24).