Generative models on phase space

• URL: http://arxiv.org/abs/2604.02415v1
• Date: Thu, 02 Apr 2026 18:00:01 GMT
• Title: Generative models on phase space
• Abstract summary: Deep generative models are powerful machine learning tools capable of learning and sampling from high-dimensional distributions.<n>We introduce generative models which are 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.<n>We demonstrate that our models are able to learn both few-particle and many-particle distributions with various singularity structures.
• Score: 1.739856067884508
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Weighted Stochastic Differential Equation to Implement Wasserstein-Fisher-Rao Gradient Flow [0.0]
  A promising line of work leverages tools from information geometry to augment diffusion-based samplers with mass reweighting mechanisms.<n>Our work provides a preliminary but rigorous investigation of WFR-based sampling dynamics, and aims to clarify their theoretical structure as a foundation for future developments.
  arXiv  Detail & Related papers  (2025-12-19T18:31:27Z)
• When and how can inexact generative models still sample from the data manifold? [2.4664553878979185]
  Despite learning errors in the score function or the drift vector field, the generated samples appear to shift emphalong the support of the data distribution but not emphaway from it.<n>We show that the alignment of the top Lyapunov vectors with the tangent spaces along the boundary of the data manifold leads to robustness.
  arXiv  Detail & Related papers  (2025-08-11T03:24:34Z)
• Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models [50.77646970127369]
  We propose an energy-based diffusion model with a Fokker--Planck-derived regularization term to enforce consistency.<n>We demonstrate our approach by sampling and simulating multiple biomolecular systems, including fast-folding proteins.
  arXiv  Detail & Related papers  (2025-06-20T16:38:29Z)
• Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning [79.65014491424151]
  We propose a quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM)<n>It enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces.<n>This paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
  arXiv  Detail & Related papers  (2025-05-08T11:48:21Z)
• Continuous Diffusion Model for Language Modeling [64.7425225935854]
  Existing continuous diffusion models for discrete data underperform compared to discrete methods.<n>We propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution.<n>Our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models.
  arXiv  Detail & Related papers  (2025-02-17T08:54:29Z)
• Energy-Based Diffusion Language Models for Text Generation [126.23425882687195]
  Energy-based Diffusion Language Model (EDLM) is an energy-based model operating at the full sequence level for each diffusion step.<n>Our framework offers a 1.3$times$ sampling speedup over existing diffusion models.
  arXiv  Detail & Related papers  (2024-10-28T17:25:56Z)
• Learning to Approximate Particle Smoothing Trajectories via Diffusion Generative Models [16.196738720721417]
  Learning systems from sparse observations is critical in numerous fields, including biology, finance, and physics. We introduce a method that integrates conditional particle filtering with ancestral sampling and diffusion models. We demonstrate the approach in time-series generation and tasks, including vehicle tracking and single-cell RNA sequencing data.
  arXiv  Detail & Related papers  (2024-06-01T21:54:01Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• Particle clustering in turbulence: Prediction of spatial and statistical properties with deep learning [6.91821181311687]
  We simulate the dynamics of particles in the Epstein drag regime within a periodic domain of isotropic forced hydrodynamic turbulence. We train a U-Net deep learning model to predict gridded representations of the particle density and velocity fields, given as input the corresponding fluid fields. Our results suggest that, given appropriately expanded training data, deep learning could complement direct numerical simulations in predicting particle clustering within turbulent flows.
  arXiv  Detail & Related papers  (2022-10-05T15:46:28Z)
• Inference and De-Noising of Non-Gaussian Particle Distribution Functions: A Generative Modeling Approach [0.0]
  Inference on data produced by numerical simulations generally consists of binning the data to recover the particle distribution function. Here we demonstrate the use of normalizing flows to learn a smooth, tractable approximation to the noisy particle distribution function.
  arXiv  Detail & Related papers  (2021-10-05T16:38:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.