Physics of Motion, Geometry of Cohesion: A Silky Gaussian Head Avatar Framework

We present <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Physics of Motion, Geometry of Cohesion</i>, a framework for creating high-fidelity, dynamic 3D Gaussian head avatars free from common motion and geometry artifacts. To capture the “Physics of Motion,” we introduce a physics-guided propagation module using second-order kinematics (means) and Lie group transformation (covariances) to generate plausible deformation priors. These priors inform a data-driven refinement network. For “Geometry of Cohesion,” we employ a hierarchical Optimal Transport (OT) regularization strategy. Grouping Gaussians by facial landmarks and using adaptive, hyperbolically weighted OT costs ensures spatiotemporal consistency while preserving local expressiveness. Experimental results demonstrate this synergistic approach effectively mitigates common artifacts like jitter and tearing, significantly reducing irregular deformations. This yields high-fidelity, dynamic avatars characterized by natural facial motion and a temporally coherent, “silky” visual quality.