基于轨道空间粒子流匹配的生成建模

摘要

我们提出轨道空间几何概率路径（OGPP），这是一种面向粒子系统的原生粒子流匹配生成建模框架。OGPP的提出基于两个关键洞见：（i）粒子具有置换对称性，匿名索引会放大每个索引的目标方差，导致生成弯曲且难以学习的流；（ii）粒子存在于物理空间，其流终端速度具有物理意义，能够编码几何属性（如表面法线）。OGPP实现了三大核心组件：（1）概率路径终端端点的轨道空间规范化；（2）用于角色专门化的粒子索引嵌入；（3）具备弧长感知终端速度的几何概率路径，可在生成过程中同步产生法线。我们在极小曲面基准测试中验证OGPP，其单步推理可将度量误差降低两个数量级；在ShapeNet数据集上，仅用五分之一步数即可达到当前最优水平，并以26倍更少参数和5倍更少步数实现与DiT-3D相当的飞机点云EMD指标；在单形状编码任务中，该框架完全在三维空间运行，却能生成与6D生成器相媲美的法线和重建结果。

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.

基于轨道空间粒子流匹配的生成建模

Generative Modeling with Orbit-Space Particle Flow Matching

摘要

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