{"paper_id":"2fb389af-b172-4d3d-8138-ee850c6aeec2","body_text":"Denoising Diffusion Probabilistic Model-Based Multivariate Parameter Distributions for Rough Discrete Fracture Network Modeling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Denoising Diffusion Probabilistic Model-Based Multivariate Parameter Distributions for Rough Discrete Fracture Network Modeling Shuyang Han, Jiajun Wang, Dawei Tong, Xiaoling Wang, Wanyu Zhang, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6333508/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Fractures significantly influence rock mass geotechnical behavior, necessitating precise characterization of their geometric parameters. Traditional modeling approaches, based on standard statistical descriptions and random simulations, often disregard parameter correlations and assume smooth fractures, compromising accuracy. This study introduces a Denoising Diffusion Probabilistic Model (DDPM) to capture dip direction, dip angle, trace length, aperture, and roughness correlations and generate discrete fracture network (DFN) modeling data. By integrating fractal dimensions and non-uniform rational B-splines (NURBS) tensor products, our approach accommodates fracture roughness, enhancing overall realism. Validation on real-world datasets using Kullback–Leibler(KL) divergence and Wasserstein distance indicates that DDPM significantly outperforms generative adversarial networks (GAN), variational autoencoders (VAE), normalizing flow (NF), and Monte Carlo methods, achieving average KL/Wasserstein distance reductions of 72.44%/57.08% against other generative models and 74.84%/36.83% against Monte Carlo. Furthermore, the modeled rough fractures accurately match the roughness of real fracture traces, confirming the improved fidelity of the DFN simulations. Multivariate distribution Generative model Denoising diffusion probabilistic model Rough discrete fracture network (RDFN) Correlation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-6333508\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":435679480,\"identity\":\"b92b31e0-de15-45b4-ad46-5df6ef891d0f\",\"order_by\":0,\"name\":\"Shuyang Han\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Tianjin University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Shuyang\",\"middleName\":\"\",\"lastName\":\"Han\",\"suffix\":\"\"},{\"id\":435679481,\"identity\":\"f829dd4a-09e7-4051-8406-987c79eea2b9\",\"order_by\":1,\"name\":\"Jiajun 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Traditional modeling approaches, based on standard statistical descriptions and random simulations, often disregard parameter correlations and assume smooth fractures, compromising accuracy. This study introduces a Denoising Diffusion Probabilistic Model (DDPM) to capture dip direction, dip angle, trace length, aperture, and roughness correlations and generate discrete fracture network (DFN) modeling data. By integrating fractal dimensions and non-uniform rational B-splines (NURBS) tensor products, our approach accommodates fracture roughness, enhancing overall realism. Validation on real-world datasets using Kullback\\u0026ndash;Leibler(KL) divergence and Wasserstein distance indicates that DDPM significantly outperforms generative adversarial networks (GAN), variational autoencoders (VAE), normalizing flow (NF), and Monte Carlo methods, achieving average KL/Wasserstein distance reductions of 72.44%/57.08% against other generative models and 74.84%/36.83% against Monte Carlo. 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