Combining complex Langevin dynamics with score-based and energy-based diffusion models

Aarts, Gert; Habibi, Diaa Eddin; Wang, Lingxiao; Zhou, Kai

doi:10.1007/jhep12(2025)160

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Combining complex Langevin dynamics with score-based and energy-based diffusion models

Gert Aarts

, Diaa Eddin Habibi, Lingxiao Wang

, Kai Zhou

Journal of High Energy Physics, Volume: 2025, Issue: 12, Start page: 160

Swansea University Authors: Gert Aarts , Diaa Eddin Habibi

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DOI (Published version): 10.1007/jhep12(2025)160

Abstract

Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notori...

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Published in:	Journal of High Energy Physics
ISSN:	1029-8479
Published:	Springer Nature 2025
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa71204

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spelling	2026-01-07T16:10:34.1447383 v2 71204 2026-01-07 Combining complex Langevin dynamics with score-based and energy-based diffusion models 1ba0dad382dfe18348ec32fc65f3f3de 0000-0002-6038-3782 Gert Aarts Gert Aarts true false 5d736de7adfea5495e2e56a4dcb42524 Diaa Eddin Habibi Diaa Eddin Habibi true false 2026-01-07 BGPS Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notoriously hard to understand. In generative AI, diffusion models can learn distributions, or their log derivatives, from data. We explore the ability of diffusion models to learn the distributions sampled by a complex Langevin process, comparing score-based and energy-based diffusion models, and speculate about possible applications. Journal Article Journal of High Energy Physics 2025 12 160 Springer Nature 1029-8479 Algorithms and Theoretical Developments; Non-Zero Temperature and Density; Other Lattice Field Theories 22 12 2025 2025-12-22 10.1007/jhep12(2025)160 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University Other GA thanks KZ and his group for the kind hospitality at CUHK-Shenzhen during the completion of this work. This visit was supported in part by the Royal Society International Exchanges 2024 Global Round 2 IES\R2\242215. GA is further supported by STFC Consolidated Grant ST/X000648/1. DEH is supported by the UKRI AIMLAC CDT EP/S023992/1. LW thanks the DEEP-IN working group at RIKEN-iTHEMS for its support in the preparation of this paper. LW is also supported by the RIKEN TRIP initiative (RIKEN Quantum), JSPS KAKENHI Grant No. 25H01560, and JST-BOOST Grant No. JPMJBY24H9. KZ is supported by the CUHK-Shenzhen university development fund under grant No. UDF01003041 and UDF03003041, Shenzhen Peacock fund under No. 2023TC0179 and NSFC grant under No. 92570117. We acknowledge the support of the Supercomputing Wales and AccelerateAI projects, which are part-funded by the European Regional Development Fund (ERDF) via Welsh Government. Article funded by SCOAP3. 2026-01-07T16:10:34.1447383 2026-01-07T15:59:43.2470315 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Gert Aarts 0000-0002-6038-3782 1 Diaa Eddin Habibi 2 Lingxiao Wang 0000-0003-3757-3403 3 Kai Zhou 0000-0001-9859-1758 4 71204__35913__7dfe7c2b66e249bd80ba0b94f8059a20.pdf 71204.VOR.pdf 2026-01-07T16:07:19.9651610 Output 3598115 application/pdf Version of Record true © The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY4.0). true eng http://creativecommons.org/licenses/by/4.0/
title	Combining complex Langevin dynamics with score-based and energy-based diffusion models
spellingShingle	Combining complex Langevin dynamics with score-based and energy-based diffusion models Gert Aarts Diaa Eddin Habibi
title_short	Combining complex Langevin dynamics with score-based and energy-based diffusion models
title_full	Combining complex Langevin dynamics with score-based and energy-based diffusion models
title_fullStr	Combining complex Langevin dynamics with score-based and energy-based diffusion models
title_full_unstemmed	Combining complex Langevin dynamics with score-based and energy-based diffusion models
title_sort	Combining complex Langevin dynamics with score-based and energy-based diffusion models
author_id_str_mv	1ba0dad382dfe18348ec32fc65f3f3de 5d736de7adfea5495e2e56a4dcb42524
author_id_fullname_str_mv	1ba0dad382dfe18348ec32fc65f3f3de_*_Gert Aarts 5d736de7adfea5495e2e56a4dcb42524_*_Diaa Eddin Habibi
author	Gert Aarts Diaa Eddin Habibi
author2	Gert Aarts Diaa Eddin Habibi Lingxiao Wang Kai Zhou
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container_title	Journal of High Energy Physics
container_volume	2025
container_issue	12
container_start_page	160
publishDate	2025
institution	Swansea University
issn	1029-8479
doi_str_mv	10.1007/jhep12(2025)160
publisher	Springer Nature
college_str	Faculty of Science and Engineering
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department_str	School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
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description	Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notoriously hard to understand. In generative AI, diffusion models can learn distributions, or their log derivatives, from data. We explore the ability of diffusion models to learn the distributions sampled by a complex Langevin process, comparing score-based and energy-based diffusion models, and speculate about possible applications.
published_date	2025-12-22T05:34:42Z
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score	11.096212

Combining complex Langevin dynamics with score-based and energy-based diffusion models

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