  Meshes are important representations of physical 3D entities in the virtual
world. Applications like rendering, simulations and 3D printing require meshes
to be manifold so that they can interact with the world like the real objects
they represent. Prior methods generate meshes with great geometric accuracy but
poor manifoldness. In this work, we propose Neural Mesh Flow (NMF) to generate
two-manifold meshes for genus-0 shapes. Specifically, NMF is a shape
auto-encoder consisting of several Neural Ordinary Differential Equation
(NODE)[1] blocks that learn accurate mesh geometry by progressively deforming a
spherical mesh. Training NMF is simpler compared to state-of-the-art methods
since it does not require any explicit mesh-based regularization. Our
experiments demonstrate that NMF facilitates several applications such as
single-view mesh reconstruction, global shape parameterization, texture
mapping, shape deformation and correspondence. Importantly, we demonstrate that
manifold meshes generated using NMF are better-suited for physically-based
rendering and simulation. Code and data are released.
