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

arXiv: https://arxiv.org/abs/2511.10793 · HTML: https://mlsanity.com/paper/2511.10793/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 13 Nov 2025.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 19 of 19)

- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing](https://mlsanity.com/paper/2110.13900/) (2021)
- [Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale](https://mlsanity.com/paper/2306.15687/) (2023)
- [Efficient Training of Audio Transformers with Patchout](https://mlsanity.com/paper/2110.05069/) (2021)
- [ASVspoof 2019: Future Horizons in Spoofed and Fake Audio Detection](https://mlsanity.com/paper/1904.05441/) (2019)
- [VoiceFlow: Efficient Text-to-Speech with Rectified Flow Matching](https://mlsanity.com/paper/2309.05027/) (2023)
- [Audio Deepfake Detection with Self-Supervised WavLM and Multi-Fusion Attentive Classifier](https://mlsanity.com/paper/2312.08089/) (2023)
- [ReFlow-TTS: A Rectified Flow Model for High-fidelity Text-to-Speech](https://mlsanity.com/paper/2309.17056/) (2023)
- [DFADD: The Diffusion and Flow-Matching Based Audio Deepfake Dataset](https://mlsanity.com/paper/2409.08731/) (2024)
- [DiffProsody: Diffusion-based Latent Prosody Generation for Expressive Speech Synthesis with Prosody Conditional Adversarial Training](https://mlsanity.com/paper/2307.16549/) (2023)
- [CM-TTS: Enhancing Real Time Text-to-Speech Synthesis Efficiency through Weighted Samplers and Consistency Models](https://mlsanity.com/paper/2404.00569/) (2024)
- [People are poorly equipped to detect AI-powered voice clones](https://mlsanity.com/paper/2410.03791/) (2024)
- [Comprehensive Layer-wise Analysis of SSL Models for Audio Deepfake Detection](https://mlsanity.com/paper/2502.03559/) (2025)
- [DiffAR: Denoising Diffusion Autoregressive Model for Raw Speech Waveform Generation](https://mlsanity.com/paper/2310.01381/) (2023)
- [USAD: Universal Speech and Audio Representation via Distillation](https://mlsanity.com/paper/2506.18843/) (2025)
- [Source Tracing of Synthetic Speech Systems Through Paralinguistic Pre-Trained Representations](https://mlsanity.com/paper/2506.01157/) (2025)
- [Towards Source Attribution of Singing Voice Deepfake with Multimodal Foundation Models](https://mlsanity.com/paper/2506.03364/) (2025)

## Built on by (most cited first, 1 of 1)

- [Disentangling Speaker Traits for Deepfake Source Verification via Chebyshev Polynomial and Riemannian Metric Learning](https://mlsanity.com/paper/2603.21875/) (2026)

## Abstract (arXiv)

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.