  This paper introduces Neural Subdivision, a novel framework for data-driven
coarse-to-fine geometry modeling. During inference, our method takes a coarse
triangle mesh as input and recursively subdivides it to a finer geometry by
applying the fixed topological updates of Loop Subdivision, but predicting
vertex positions using a neural network conditioned on the local geometry of a
patch. This approach enables us to learn complex non-linear subdivision
schemes, beyond simple linear averaging used in classical techniques. One of
our key contributions is a novel self-supervised training setup that only
requires a set of high-resolution meshes for learning network weights. For any
training shape, we stochastically generate diverse low-resolution
discretizations of coarse counterparts, while maintaining a bijective mapping
that prescribes the exact target position of every new vertex during the
subdivision process. This leads to a very efficient and accurate loss function
for conditional mesh generation, and enables us to train a method that
generalizes across discretizations and favors preserving the manifold structure
of the output. During training we optimize for the same set of network weights
across all local mesh patches, thus providing an architecture that is not
constrained to a specific input mesh, fixed genus, or category. Our network
encodes patch geometry in a local frame in a rotation- and
translation-invariant manner. Jointly, these design choices enable our method
to generalize well, and we demonstrate that even when trained on a single
high-resolution mesh our method generates reasonable subdivisions for novel
shapes.
