Spherical Geometry Diffusion: Generating High-quality 3D Face Geometry via Sphere-anchored Representations

A fundamental challenge in text-to-3D face generation is achieving high-quality geometry. The core difficulty lies in the arbitrary and intricate distribution of vertices in 3D space, making it challenging for existing models to establish clean connectivity and resulting in suboptimal geometry. To address this, our core insight is to simplify the underlying geometric structure by constraining the distribution onto a simple and regular manifold, a topological sphere. Building on this, we first propose the Spherical Geometry Representation, a novel face representation that anchors geometric signals to uniform spherical coordinates. This guarantees a regular point distribution, from which the mesh connectivity can be robustly reconstructed. Critically, this canonical sphere can be seamlessly unwrapped into a 2D map, creating a perfect synergy with powerful 2D generative models. We then introduce Spherical Geometry Diffusion, a conditional diffusion framework built upon this 2D map. It enables diverse and controllable generation by jointly modeling geometry and texture, where the geometry explicitly conditions the texture synthesis process. Our method's effectiveness is demonstrated through its success in a wide range of tasks: text-to-3D generation, face reconstruction, and text-based 3D editing. Extensive experiments show that our approach substantially outperforms existing methods in geometric quality, textual fidelity, and inference efficiency.