BVHMesh: Face-First Mesh Generation on a Bounding Volume Hierarchy

Artist-style meshes are compact and editable, but generating their continuous geometry and irregular connectivity efficiently remains challenging. Field-based methods extract dense tessellations, whereas autoregressive methods directly generate compact meshes but decode sequentially. Recent flow-based methods generate vertices in parallel and then recover faces from predicted connectivity, where edge errors can propagate into invalid surfaces. We introduce BVHMesh as a face-first flow-based framework that decodes triangles in parallel and stitches them into a mesh. To make triangle prediction tractable, we organize triangles in an octree-aligned bounding volume hierarchy (OctBVH). Its nested boxes provide local coordinate frames for coarse-to-fine geometry prediction, while octree alignment allows sparse convolutions to process the hierarchy. A hierarchical VAE and conditional flow priors generate triangle soups from point clouds or images. EdgeMatch then recovers connectivity through learned half-edge matching with explicit checks against non-manifold edges, duplicate faces, and collapsed triangles. On Toys4K, BVHMesh achieves state-of-the-art VAE reconstruction and artist-mesh generation under both point-cloud and image conditioning. In point-cloud generation, its non-manifold edge ratio is zero versus $11.50\%$ for MeshFlow, while inference takes about $15$ seconds per mesh even beyond $10,000$ faces.