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Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>\n                    We present\n                    <jats:bold>Orbit-Space Geometric Probability Paths (OGPP)<\/jats:bold>\n                    , a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to\n                    <jats:italic toggle=\"yes\">permutation symmetries<\/jats:italic>\n                    , so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; (ii) particles live in physical space, so the flow's\n                    <jats:italic toggle=\"yes\">terminal velocity<\/jats:italic>\n                    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 5\u00d7 fewer steps and reaches airplane EMD comparable to DiT-3D with 26\u00d7 fewer parameters and 5\u00d7 fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.\n                  <\/jats:p>","DOI":"10.1145\/3811342","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Generative Modeling with Orbit-Space Particle Flow Matching"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9322-2351","authenticated-orcid":false,"given":"Sinan","family":"Wang","sequence":"first","affiliation":[{"name":"Georgia Institute of Technology, ATLANTA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-4319-1191","authenticated-orcid":false,"given":"Jinjin","family":"He","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, ATLANTA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-2819-0254","authenticated-orcid":false,"given":"Shenyifan","family":"Lu","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, ATLANTA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6119-1544","authenticated-orcid":false,"given":"Ruicheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, ATLANTA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3419-6369","authenticated-orcid":false,"given":"Greg","family":"Turk","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, ATLANTA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1392-0928","authenticated-orcid":false,"given":"Bo","family":"Zhu","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, ATLANTA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"International conference on machine learning. 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