Generative models on phase space

2026-04-02

AI Summary

Existing generative models struggle to rigorously enforce strong physical priors such as energy-momentum conservation in high-energy physics, limiting their interpretability and reliability. This work proposes a novel generative framework that, for the first time, integrates diffusion and flow matching methods within the center-of-mass frame on the massless N-particle Lorentz-invariant phase space manifold. By initializing with a uniform distribution over phase space and enforcing exact conservation laws at every step of the sampling trajectory, the model seamlessly incorporates the geometric structure and manifold constraints of phase space. This approach successfully captures both few- and many-body distributions featuring complex singularities, establishing a foundation for interpretable, simulation-based generative modeling of jet observables.

Abstract

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be concentrated on a submanifold of the data embedding space. For high-energy physics data, consisting of collections of relativistic energy-momentum 4-vectors, this submanifold can enforce extremely strong physically-motivated priors, such as energy and momentum conservation. If these constraints are learned only approximately, rather than exactly, this can inhibit the interpretability and reliability of such generative models. To remedy this deficiency, we introduce generative models which are, by construction, confined at every step of their sampling trajectory to the manifold of massless N-particle Lorentz-invariant phase space in the center-of-momentum frame. In the case of diffusion models, the "pure noise" forward process endpoint corresponds to the uniform distribution on phase space, which provides a clear starting point from which to identify how correlations among the particles emerge during the reverse (de-noising) process. We demonstrate that our models are able to learn both few-particle and many-particle distributions with various singularity structures, paving the way for future interpretability studies using generative models trained on simulated jet data.

Problem

• generative models
• phase space
• Lorentz invariance
• energy-momentum conservation
• high-energy physics

Innovation

• phase space
• generative models
• Lorentz invariance
• diffusion models
• energy-momentum conservation