Generative Modeling with Orbit-Space Particle Flow Matching

TL;DR

OGPP introduces a particle-native flow-matching framework that leverages physical space and symmetry considerations to improve generative modeling of particle systems, achieving significant accuracy and efficiency gains.

Contribution

It proposes a novel orbit-space geometric probability path framework with canonicalization and role-specific embeddings for better particle system modeling.

Findings

Reduces metric error by up to two orders of magnitude on minimal-surface benchmarks.

Matches state-of-the-art performance on ShapeNet with fewer steps and parameters.

Produces normals and reconstructions comparable to 6D generators in 3D.

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 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.