  Geometry is a ubiquitous language of computer graphics, design, and
engineering. However, the lack of large shape datasets limits the application
of state-of-the-art supervised learning methods and motivates the exploration
of alternative learning strategies. To this end, we introduce geometry-informed
neural networks (GINNs) to train shape generative models \emph{without any
data}. GINNs combine (i) learning under constraints, (ii) neural fields as a
suitable representation, and (iii) generating diverse solutions to
under-determined problems. We apply GINNs to several two and three-dimensional
problems of increasing levels of complexity. Our results demonstrate the
feasibility of training shape generative models in a data-free setting. This
new paradigm opens several exciting research directions, expanding the
application of generative models into domains where data is sparse.
