Closed-form conditional diffusion models for data assimilation

Closed-form conditional diffusion models for data assimilation | 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 Closed-form conditional diffusion models for data assimilation Brianna Binder, Agnimitra Dasgupta, Assad Oberai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9116949/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new samples from the data distribution by reversing a noise injection process. While it is common to train neural networks to approximate the score function, we leverage the analytical tractability of the score function to assimilate the states of a system with measurements. To enable the efficient evaluation of the score function , we use kernel density estimation to model the joint distribution of the states and their corresponding measurements. The proposed approach also inherits the capability of conditional diffusion models of operating in black-box settings, i.e., the proposed data assimilation approach can accommodate systems and measurement processes without their explicit knowledge. The ability to accommodate black-box systems combined with the superior capabilities of diffusion models in approximating complex, non-Gaussian probability distributions means that the proposed approach offers advantages over many widely used filtering methods. We evaluate the proposed method on nonlinear data assimilation problems based on the Lorenz-63 and Lorenz-96 systems of moderate dimensionality and non-linear measurement models. Results show the proposed approach outperforms the widely used ensemble Kalman and particle filters when small to moderate ensemble sizes are used. Data assimilation Bayesian filtering generative models diffusion models Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 21 Apr, 2026 Reviews received at journal 18 Apr, 2026 Reviewers agreed at journal 08 Apr, 2026 Reviewers invited by journal 24 Mar, 2026 Editor assigned by journal 18 Mar, 2026 Submission checks completed at journal 16 Mar, 2026 First submitted to journal 13 Mar, 2026 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-9116949","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":608465078,"identity":"843acfdb-4d11-46c9-9dc0-a60de419142e","order_by":0,"name":"Brianna Binder","email":"","orcid":"","institution":"University of Southern California","correspondingAuthor":false,"prefix":"","firstName":"Brianna","middleName":"","lastName":"Binder","suffix":""},{"id":608465081,"identity":"73912ea4-046f-4987-a8a4-f9f418d9f64f","order_by":1,"name":"Agnimitra Dasgupta","email":"","orcid":"","institution":"Sandia National Laboratories","correspondingAuthor":false,"prefix":"","firstName":"Agnimitra","middleName":"","lastName":"Dasgupta","suffix":""},{"id":608465084,"identity":"b23fb20f-788e-4cc2-a423-75e1f1497480","order_by":2,"name":"Assad Oberai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsklEQVRIiWNgGAWjYFACHhAhIQfhsJGgxZhkLQyJDURr4W/vPfi4osYifcP5ww8YPpQdJqxF4sy5ZMMzxyRyN9xIM2CccY4ILQw3cswkG9hAWngYmHnbiNAifyPH/GfDP4l0g/NnGJj/EqPFAGgLY2ObRILBgRwGZkZitBgC/SLZ2CdhOBPol4M959IJa5E73nvwY8O3Onm+84cfPvhRZk1YCwo4QKL6UTAKRsEoGAW4AAAPeDsOdYNZCAAAAABJRU5ErkJggg==","orcid":"","institution":"University of Southern California","correspondingAuthor":true,"prefix":"","firstName":"Assad","middleName":"","lastName":"Oberai","suffix":""}],"badges":[],"createdAt":"2026-03-13 17:08:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9116949/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9116949/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105564587,"identity":"04e5f194-bd0b-4b47-83c1-25e41ea4bd0e","added_by":"auto","created_at":"2026-03-27 12:50:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2972837,"visible":true,"origin":"","legend":"","description":"","filename":"GMMDataAssimilationsubmitted.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9116949/v1_covered_3eb94067-0fe5-430c-8beb-a2ab6d2bee70.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Closed-form conditional diffusion models for data assimilation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"engineering-with-computers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ewco","sideBox":"Learn more about [Engineering with Computers](http://link.springer.com/journal/366)","snPcode":"366","submissionUrl":"https://submission.nature.com/new-submission/366/3","title":"Engineering with Computers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Data assimilation, Bayesian filtering, generative models, diffusion models","lastPublishedDoi":"10.21203/rs.3.rs-9116949/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9116949/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We propose closed-form conditional diffusion models for data assimilation. 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