Generative Modeling with Orbit-Space Particle Flow Matching
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917457367662592 |
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| author | Wang, Sinan He, Jinjin Lu, Shenyifan Wang, Ruicheng Turk, Greg Zhu, Bo |
| author_facet | Wang, Sinan He, Jinjin Lu, Shenyifan Wang, Ruicheng Turk, Greg Zhu, Bo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_02222 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generative Modeling with Orbit-Space Particle Flow Matching Wang, Sinan He, Jinjin Lu, Shenyifan Wang, Ruicheng Turk, Greg Zhu, Bo Graphics Computer Vision and Pattern Recognition 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. |
| title | Generative Modeling with Orbit-Space Particle Flow Matching |
| topic | Graphics Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2605.02222 |