新方法让粒子生成更准更快，一步就能大幅降低误差。
Generative Modeling with Orbit-Space Particle Flow Matching
- 用轨道空间归一化消除粒子顺序干扰，让生成路径更平滑。
- 单步生成即达最优，表面误差降两数量级，3D形状重建更优。
- 适合做高精度3D生成，尤其擅长生成法向等几何特征。
我们提出轨道空间几何概率路径（OGPP），一种面向粒子系统的原生粒子流匹配生成模型框架。其核心洞察为：(i) 粒子具有置换对称性，传统索引方式会放大目标方差，导致路径弯曲、难学习；(ii) 粒子位于物理空间中，终态速度具物理意义，可编码几何属性如表面法向。OGPP包含三个关键组件：(1) 概率路径终点的轨道空间归一化；(2) 粒子索引嵌入实现角色分化；(3) 弧长感知的几何概率路径，生成过程中自然产出法向。在最小曲面基准测试中，单次推理即减少度量误差两个数量级；在ShapeNet上，仅需5倍少步骤即达当前最优，飞机点云EMD媲美DiT-3D，但参数量减少26倍、推理步骤减少5倍；在单形状编码任务中，生成的法向与重建质量媲美6D生成器，且全程运行于3D空间。
原文摘要 · Abstract (English)
We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.
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