Paper Detail
Sinan Wang, Jinjin He, Shenyifan Lu, Ruicheng Wang, Greg Turk, Bo Zhu
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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@misc{wang2026generative,
title = {Generative Modeling with Orbit-Space Particle Flow Matching},
author = {Sinan Wang and Jinjin He and Shenyifan Lu and Ruicheng Wang and Greg Turk and Bo Zhu},
year = {2026},
abstract = {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 instant},
url = {https://huggingface.co/papers/2605.02222},
keywords = {particle-native, flow-matching framework, generative modeling, orbit-space canonicalization, particle index embeddings, geometric probability paths, arc-length-aware terminal velocities, particle systems, probability-path terminal endpoint, role specialization, surface normals, minimal-surface benchmarks, ShapeNet, DiT-3D, EMD, 6D generators, 3D reconstruction, huggingface daily},
eprint = {2605.02222},
archiveprefix = {arXiv},
}
{}