FuzzyGS: Fuzzy-Based Geometric Uncertainty Gaussian Splatting for Fast Talking Head Synthesis

3-D Gaussian Splatting has demonstrated impressive performance in talking head synthesis. However, there remain two practical limitations: First, existing methods focus solely on deforming isolated Gaussian primitives to model dynamic Gaussian attributes, while ignoring uncertainty motion correlations among neighboring Gaussian primitives, leading to unrealistic facial movements. Second, they consume substantial resources due to the overreliance on full model optimization for each identity individually, thereby restricting their applicability in practical scenarios. To tackle these limitations, we propose a novel Fuzzy-based geometric uncertainty Gaussian splatting scheme, named FuzzyGS, for audio-driven talking head synthesis, which not only maintains vivid and realistic rendering but also promotes efficiency. Specifically, to improve the realism of facial motion, we develop a geometric-aware fuzzy fusion strategy that explicitly models fuzzy geometric relations among neighboring Gaussian primitives, effectively facilitating their mutual perception and coordinated deformation. Furthermore, to alleviate the computational cost, we design a two-stage learning strategy, which first learns unified motion prior applicable to most identities, and then achieves motion adaptive alignment through fine-tuning stage for quickly adapting to any new identity. Benefiting from the above elaborate designs, our method achieves high-fidelity talking head synthesis while improving efficiency. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art methods both quantitatively and qualitatively.