Reproduce “Generative Modeling with Orbit-Space Particle Flow Matching” on OpenResearch

About this paper

Sinan Wang, Jinjin He, Shenyifan Lu, Ruicheng Wang, Greg Turk, Bo Zhu

A "particle-native" flow-matching framework, Orbit-Space Geometric Probability Paths (OGPP), is presented for generating particle systems and 3D shapes. OGPP achieves high quality results in energy-driven particle generation and 3D shape synthesis, producing accurate point clouds and surface normals with significantly fewer inference steps compared to existing flow-matching methods.

Key insights

• Canonicalizing only the target distribution ($X_1$) for permutation symmetry, rather than both endpoints, significantly reduces target variance and yields "straighter," easier-to-learn probability flows.
• The terminal velocity of a probability path can be leveraged to intrinsically encode geometric attributes, such as surface normals, making them a direct byproduct of the generative process.
• Treating particles from a Lagrangian perspective, with explicit mechanisms for handling permutation symmetry and physical semantics, leads to a more structured and efficient learning problem for generative models.

Summary by alphaXiv.