学习层级双曲混合模型用于部件感知三维生成
Learning Hierarchical Hyperbolic Mixture Model for Part-aware 3D Generation
把部件层级语义嵌入双曲流形并用测地线扩散生成，配合黎曼高阶求解器加速扩散 ODE，可为需要层级结构先验的 3D 生成/重建提供可复用的表征与采样方案。
原文依据 we propose a novel framework for hierarchical and efficient part-aware 3D generation in hyperbolic space
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论三维形状生成在图形学与视觉应用中日益重要。当前的部件感知三维生成通常忽略部件间的层级关系，或在欧氏空间中低效地编码多层级语义。为此，我们提出一个在双曲空间中实现层级化且高效的部件感知三维生成的新框架。我们的贡献有三方面：（1）层级双曲混合模型（H^2MM）：我们提出双曲流形内物体的部件感知语义表示，为物体细节与语义提供高保真的层级部件感知表示。（2）双曲语义一致扩散模型：我们设计测地线扩散过程，以保持 H^2MM 的层级与语义结构，并从条件中逐步生成语义、在其联合引导下生成物体。我们使用自适应树结构神经网络，以放宽先前双曲扩散中联合生成节点与边的约束。（3）双曲扩散模型求解器：我们利用双曲流形上的高阶黎曼梯度，为扩散 ODE 设计快速专用的高阶求解器，并具有收敛阶保证。大量实验表明，我们的方法在质量与效率上均取得更优表现。
英文原文摘要 1338 字符
3D shape generation has become increasingly important for graphics and vision applications. Current part-aware 3D generation usually overlooks hierarchical part relations or inefficiently encodes multi-level semantics in Euclidean space. Thus we propose a novel framework for hierarchical and efficient part-aware 3D generation in hyperbolic space. Our contributions are three-fold: (1) Hierarchical Hyperbolic Mixture Model (H^2MM): We propose part-aware semantic representation of objects within a hyperbolic manifold, providing a high-fidelity hierarchical part-aware representation of object details and semantics. (2) Hyperbolic Semantically Consistent Diffusion Model: We design the geodesic diffusion process that preserves the hierarchical and semantic structure of H^ 2 MM, and progressively generates semantics from conditions and generates object under their joint guidance. We use an adaptive tree-structured neural network to loosen the constraint of jointly generating nodes and edges in previous hyperbolic diffusion. (3) Hyperbolic Diffusion Model Solver: We leverage higher-order Riemannian gradient on hyperbolic manifolds for designing a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. Extensive experiments demonstrate that our method achieves superior quality and efficiency.