We investigate the problem of training generative models on a very sparse collection of 3D models. We use geometrically motivated energies to augment and thus boost a sparse collection of example (training) models.

We analyze the Hessian of the as-rigid-as-possible (ARAP) energy to sample from and project to the underlying (local) shape space, and use the augmented dataset to train a variational autoencoder (VAE). We iterate the process of building latent spaces of VAE and augmenting the associated dataset, to progressively reveal a richer and more expressive generative space for creating geometrically and semantically valid samples.

Our framework allows us to train generative 3D models even with a small set of good quality 3D models, which are typically hard to curate. We extensively evaluate our method against a set of strong baselines, provide ablation studies and demonstrate application towards establishing shape correspondences.

We present multiple examples of interesting and meaningful shape variations even when starting from as few as 3-10 training shapes.