让扩散模型学会在球面数据上保持角度结构，生成更准确。
Harmonizing Geometry and Uncertainty: Diffusion with Hyperspheres
- 用方向性噪声替代传统高斯噪声，匹配球面数据几何
- 在4个物体和2个人脸数据集上提升球面流形保持能力
- 适合处理角度敏感的视觉生成任务，如姿态或方向建模
当前扩散模型在前向过程依赖各向同性的高斯噪声，本质上适用于欧几里得空间，但许多真实数据（如超球面流形）具有角几何特性。在欧氏空间中建模时，这些角度细节会丢失，导致生成性能下降。为此，我们提出HyperSphereDiff，通过引入方向性噪声来对齐超球面结构，保留类别几何并有效捕捉角度不确定性。理论与实证均表明，该方法使生成过程与超球面数据的内在几何一致，显著提升生成质量。我们在四个物体数据集和两个人脸数据集上验证了该框架的有效性，结果表明引入角度不确定性能更好保持底层超球面流形。代码资源见：https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/
原文摘要 · Abstract (English)
Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems involve non-Euclidean distributions, such as hyperspherical manifolds, where class-specific patterns are governed by angular geometry within hypercones. When modeled in Euclidean space, these angular subtleties are lost, leading to suboptimal generative performance. To address this limitation, we introduce HyperSphereDiff to align hyperspherical structures with directional noise, preserving class geometry and effectively capturing angular uncertainty. We demonstrate both theoretically and empirically that this approach aligns the generative process with the intrinsic geometry of hyperspherical data, resulting in more accurate and geometry-aware generative models. We evaluate our framework on four object datasets and two face datasets, showing that incorporating angular uncertainty better preserves the underlying hyperspherical manifold. Resources are available at: {https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/}
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。