- Open Access
Diffusion-based point-cloud generation of heavy-ion events
Phys. Rev. C 114, 024904 – Published 10 August, 2026
DOI: https://doi.org/10.1103/nmmz-bwcs
Abstract
Heavy-ion collisions produce final states with thousands to tens of thousands of particles, making their simulation among the most computationally intensive tasks in high-energy nuclear physics. We present a fast, high-fidelity generative model for heavy-ion events based on a score-driven diffusion process and the point-edge transformer architecture within the OmniLearn framework. A two-stage training strategy is performed: Stage 1 trains on lower-multiplicity O-O collisions, allowing the model to learn a stable event-and-particles representation; this is followed in Stage 2 by fine tuning on challenging high-multiplicity Pb-Pb collisions. We benchmark the generator with a broad set of closure checks, including agreement of event- and particle-level observables in one and two dimensions, flow consistency reconstructed from the generated particles, end-to-end jet finding with FastJet including key jet and substructure observables, and a classifier-based application to quantify the sample fidelity. The results are promising, showing that a compact generative model can produce realistic, high-multiplicity heavy-ion events, at a level that makes local-scale generation for heavy-ion collisions at high energies a practical goal.
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References (29)
- Edited by I. Béjar Alonso, O. Brüning, P. Fessia, M. Lamont, L. Rossi, L. Tavian, and M. Zerlauth, High-Luminosity Large Hadron Collider (HL-LHC): Technical design report (CERN, Geneva, 2000), Vol. 10.
- H. Hirvonen, K. J. Eskola, and H. Niemi, Deep learning for flow observables in ultrarelativistic heavy-ion collisions, Phys. Rev. C 108, 034905 (2023).
- K.-Y. Wu, Z. Yang, L.-G. Pang, and X.-N. Wang, Study of jet-induced hydro response in high-energy heavy-ion collisions with a flow-matching generative model, arXiv:2605.17511.
- M. Omana Kuttan, K. Zhou, J. Steinheimer, and H. Stoecker, Ultrafast, event-by-event heavy-ion simulations for next-generation experiments, Phys. Rev. C 112, 054907 (2025).
- J.-A. Sun, L. Yan, C. Gale, and S. Jeon, End-to-end generative diffusion model for heavy-ion collisions, Phys. Rev. C 112, L051903 (2025).
- D. Torbunov, Y. Huang, M. Lin, Y. Ren, Y. Go, T. Rinn, H. Yu, B. Viren, and J. Huang, Effectiveness of denoising diffusion probabilistic models for fast and high-fidelity whole-event simulation in high-energy heavy-ion experiments, Phys. Rev. C 110, 034912 (2024).
- M. Leigh, D. Sengupta, J. A. Raine, G. Quétant, and T. Golling, Faster diffusion model with improved quality for particle cloud generation, Phys. Rev. D 109, 012010 (2024).
- V. Mikuni and B. Nachman, Method to simultaneously facilitate all jet physics tasks, Phys. Rev. D 111, 054015 (2025).
- Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, Score-based generative modeling through stochastic differential equations, arXiv:2011.13456.
- J. Y. Araz, V. Mikuni, F. Ringer, N. Sato, F. T. Acosta, and R. Whitehill, Point cloud-based diffusion models for the Electron-Ion Collider, Phys. Lett. B 868, 139694 (2025).
- T. Salimans and J. Ho, Progressive distillation for fast sampling of diffusion models, arXiv:2202.00512.
- C. Bierlich, G. Gustafson, L. Lönnblad, and H. Shah, The Angantyr model for heavy-ion collisions in Pythia8, J. High Energy Phys. 10 (2018) 134.
- C. Bierlich, S. Chakraborty, N. Desai, L. Gellersen, I. Helenius, P. Ilten, L. Lönnblad, S. Mrenna, S. Prestel, C. T. Preuss, T. Sjöstrand, P. Skands, M. Utheim, and R. Verheyen, A comprehensive guide to the physics and usage of Pythia 8.3, SciPost Phys. Codebases 2022, 8 (2022).
- M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, Glauber modeling in high-energy nuclear collisions, Annu. Rev. Nucl. Part. Sci. 57, 205 (2007).
- Perlmutter architecture, https://docs.nersc.gov/systems/perlmutter/architecture/.
- A. Sergeev and M. D. Balso, Horovod: Fast and easy distributed deep learning in TensorFlow, arXiv:1802.05799.
- M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, et al., TensorFlow: A system for large-scale machine learning, arXiv:1605.08695.
- X. Chen, C. Liang, D. Huang, E. Real, K. Wang, Y. Liu, H. Pham, X. Dong, T. Luong, C.-J. Hsieh, Y. Lu, and Q. V. Le, Symbolic discovery of optimization algorithms, arXiv:2302.06675.
- A. M. Poskanzer and S. A. Voloshin, Methods for analyzing anisotropic flow in relativistic nuclear collisions, Phys. Rev. C 58, 1671 (1998).
- M. Cacciari, G. P. Salam, and G. Soyez, The anti- jet clustering algorithm, J. High Energy Phys. 04 (2008) 063.
- M. Cacciari, G. P. Salam, and G. Soyez, FastJet user manual, Eur. Phys. J. C 72, 1896 (2012).
- A. J. Larkoski, D. Neill, and J. Thaler, Jet shapes with the broadening axis, J. High Energy Phys. 04 (2014) 017.
- Y. Dokshitzer, G. Leder, S. Moretti, and B. Webber, Better jet clustering algorithms, J. High Energy Phys. 08 (1997) 001.
- A. J. Larkoski, S. Marzani, G. Soyez, and J. Thaler, Soft drop, J. High Energy Phys. 05 (2014) 146.
- A. J. Larkoski, J. Thaler, and W. J. Waalewijn, Gaining (mutual) information about quark/gluon discrimination, J. High Energy Phys. 11 (2014) 129.
- M. Zaheer, S. Kottur, S. Ravanbakhsh, B. Poczos, R. Salakhutdinov, and A. Smola, Deep sets, arXiv:1703.06114.
- Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, Multiphase transport model for relativistic heavy ion collisions, Phys. Rev. C 72, 064901 (2005).
- OmniLearn for heavy-ion collisions, https://github.com/matplo/OmniLearn.
- R. Sadek and M. Ploskon, Data and models for: Diffusion-based point-cloud generation of heavy-ion events, Zenodo, 2026, https://doi.org/10.5281/zenodo.21402377.