  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.
