Curved Worlds, Clear Boundaries: Generalizing Speech Deepfake Detection using Hyperbolic and Spherical Geometry Spaces

In this work, we address the challenge of generalizable audio deepfake detection (ADD) across diverse speech synthesis paradigms-including conventional text-to-speech (TTS) systems and modern diffusion or flow-matching (FM) based generators. Prior work has mostly targeted individual synthesis families and often fails to generalize across paradigms due to overfitting to generation-specific artifacts. We hypothesize that synthetic speech, irrespective of its generative origin, leaves behind shared structural distortions in the embedding space that can be aligned through geometry-aware modeling. To this end, we propose RHYME, a unified detection framework that fuses utterance-level embeddings from diverse pretrained speech encoders using non-Euclidean projections. RHYME maps representations into hyperbolic and spherical manifolds-where hyperbolic geometry excels at modeling hierarchical generator families, and spherical projections capture angular, energy-invariant cues such as periodic vocoder artifacts. The fused representation is obtained via Riemannian barycentric averaging, enabling synthesis-invariant alignment. RHYME outperforms individual PTMs and homogeneous fusion baselines, achieving top performance and setting new state-of-the-art in cross-paradigm ADD.