Generative Modeling with Orbit-Space Particle Flow Matching
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| Authors | Sinan Wang et al. |
| Year | 2026 |
| HF Upvotes | 8 |
| arXiv | 2605.02222 |
| Download | |
| HF Page | View on Hugging Face |
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.
Engineering Breakdown
Plain English
This paper presents OGPP, a new approach for generating particle systems (like molecules, point clouds, or fluid simulations) using flow matching. The key innovation is treating particles as an unordered set rather than indexed objects, which reduces learning complexity and lets the model naturally output geometric properties like surface normals as a byproduct of the generation process.
Key Engineering Insight
Permutation-invariant canonicalization of particle positions eliminates artificial variance from anonymous indexing, making the flow field simpler and faster to learn. This is a straightforward architectural insight: respect the symmetries in your data structure to reduce the problem's inherent difficulty.
Why It Matters for Engineers
Particle generation is a bottleneck in physics simulation, molecular design, and 3D content creation. Current methods either ignore particle ordering (losing expressiveness) or treat them as labeled objects (creating noisy, curved learning targets). OGPP directly addresses this tradeoff, meaning faster training and better sample quality for practitioners building generative models for meshes, molecules, or point clouds.
Research Context
Flow matching has recently replaced older diffusion methods for efficiency, but prior work didn't account for particle symmetries—it treated unordered sets as if they were sequences. This paper extends flow matching to respect geometric structure and permutation invariance, enabling cleaner probability paths and opening the door for better conditional generation in physics-informed settings.
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