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Diffusion models as stochastic quantization in lattice field theory

L. Wang, Gert Aarts Orcid Logo, K. Zhou Orcid Logo

Journal of High Energy Physics, Volume: 2024, Issue: 5

Swansea University Author: Gert Aarts Orcid Logo

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DOI (Published version): 10.1007/jhep05(2024)060

Abstract

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: Springer Science and Business Media LLC 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa66440
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spelling v2 66440 2024-05-15 Diffusion models as stochastic quantization in lattice field theory 1ba0dad382dfe18348ec32fc65f3f3de 0000-0002-6038-3782 Gert Aarts Gert Aarts true false 2024-05-15 BGPS In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional φ4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles. Journal Article Journal of High Energy Physics 2024 5 Springer Science and Business Media LLC 1029-8479 Algorithms and Theoretical Developments; Lattice Quantum Field Theory; Non-Perturbative Renormalization; Stochastic Processes 7 5 2024 2024-05-07 10.1007/jhep05(2024)060 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University External research funder(s) paid the OA fee (includes OA grants disbursed by the Library) SCOAP3 2024-06-17T15:38:41.2158558 2024-05-15T09:54:35.1824902 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics L. Wang 1 Gert Aarts 0000-0002-6038-3782 2 K. Zhou 0000-0001-9859-1758 3 66440__30377__267f69f463b3494cbea2f74b532a619f.pdf jhep052024060.pdf 2024-05-15T09:59:55.2059088 Output 1451299 application/pdf Version of Record true This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0). true eng http://creativecommons.org/licenses/by/4.0/ 246
title Diffusion models as stochastic quantization in lattice field theory
spellingShingle Diffusion models as stochastic quantization in lattice field theory
Gert Aarts
title_short Diffusion models as stochastic quantization in lattice field theory
title_full Diffusion models as stochastic quantization in lattice field theory
title_fullStr Diffusion models as stochastic quantization in lattice field theory
title_full_unstemmed Diffusion models as stochastic quantization in lattice field theory
title_sort Diffusion models as stochastic quantization in lattice field theory
author_id_str_mv 1ba0dad382dfe18348ec32fc65f3f3de
author_id_fullname_str_mv 1ba0dad382dfe18348ec32fc65f3f3de_***_Gert Aarts
author Gert Aarts
author2 L. Wang
Gert Aarts
K. Zhou
format Journal article
container_title Journal of High Energy Physics
container_volume 2024
container_issue 5
publishDate 2024
institution Swansea University
issn 1029-8479
doi_str_mv 10.1007/jhep05(2024)060
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional φ4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles.
published_date 2024-05-07T15:38:39Z
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score 11.013619

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