Multi-Resolution Continuous Normalizing Flows

Multi-Resolution Continuous Normalizing Flows | 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 Multi-Resolution Continuous Normalizing Flows Vikram Voleti, Chris Finlay, Adam Oberman, Christopher Pal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3027011/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Mar, 2024 Read the published version in Annals of Mathematics and Artificial Intelligence → Version 1 posted 7 You are reading this latest preprint version Abstract Recent work has shown that Neural Ordinary Differential Equations (ODEs) can serve as generative models of images using the perspective of Continuous Normalizing Flows (CNFs). Such models offer exact likelihood calculation, and invertible generation/density estimation. In this work we introduce a Multi-Resolution variant of such models (MRCNF), by characterizing the conditional distribution over the additional information required to generate a fine image that is consistent with the coarse image. We introduce a transformation between resolutions that allows for no change in the log likelihood. We show that this approach yields comparable likelihood values for various image datasets, with improved performance at higher resolutions, with fewer parameters, using only one GPU. Further, we examine the out-of-distribution properties of MRCNFs, and find that they are similar to those of other likelihood-based generative models. Continuous Normalizing Flows Image generation wavelet Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Mar, 2024 Read the published version in Annals of Mathematics and Artificial Intelligence → Version 1 posted Editorial decision: Revision requested 14 Nov, 2023 Reviews received at journal 09 Oct, 2023 Reviewers agreed at journal 27 Aug, 2023 Reviewers invited by journal 11 Aug, 2023 Editor assigned by journal 13 Jun, 2023 Submission checks completed at journal 13 Jun, 2023 First submitted to journal 05 Jun, 2023 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. 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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-3027011","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":209657503,"identity":"3e486e87-2fb7-41db-a958-1daea2ca30e8","order_by":0,"name":"Vikram Voleti","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIie3PMQrCMBSA4YQH6aJk1UHPoLh6E5cGwcnsHVQCAV0UVwXRK+iSuRJoF8EDuNQDCLrVQTAVBZe2ugnmh4RHycejCNlsvxiQ5+CY43rJFxAfEkBYuLtkwDkEvRM8TKYcUgtJ53ztIjYFCKPjst+iI0NiT6UTTfR8ohCbS8IEUyGfabNtvDukkrJ0JCoq1KjpQt2QgAtDAA+zCb49CL0Itgj4Ko9QIBrMlqrZggUTPb7+gLShokrVsiT1mRv4fGPINutfCA0a+KSaBerI6BL3Bny519so9tLJs9Jr0I/bz3v/3uCbxzabzfYn3QFEPFQ9B/YEowAAAABJRU5ErkJggg==","orcid":"","institution":"University of Montreal","correspondingAuthor":true,"prefix":"","firstName":"Vikram","middleName":"","lastName":"Voleti","suffix":""},{"id":209657504,"identity":"39f6e74c-b3ec-41f2-bd21-e777475ad311","order_by":1,"name":"Chris Finlay","email":"","orcid":"","institution":"Deep Render","correspondingAuthor":false,"prefix":"","firstName":"Chris","middleName":"","lastName":"Finlay","suffix":""},{"id":209657505,"identity":"d71eb333-1a8e-4d8d-af8a-6faacce3215d","order_by":2,"name":"Adam Oberman","email":"","orcid":"","institution":"McGill University","correspondingAuthor":false,"prefix":"","firstName":"Adam","middleName":"","lastName":"Oberman","suffix":""},{"id":209657506,"identity":"7da4c743-f06f-47a3-9dd8-867564b8d52a","order_by":3,"name":"Christopher Pal","email":"","orcid":"","institution":"Polytechnique Montréal","correspondingAuthor":false,"prefix":"","firstName":"Christopher","middleName":"","lastName":"Pal","suffix":""}],"badges":[],"createdAt":"2023-06-06 03:59:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3027011/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3027011/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10472-024-09939-5","type":"published","date":"2024-03-21T15:01:13+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":53403636,"identity":"f0090840-40af-4e4f-9cf0-60e872c37a0b","added_by":"auto","created_at":"2024-03-25 15:13:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1073542,"visible":true,"origin":"","legend":"","description":"","filename":"MRCNFSpringer23.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3027011/v1_covered_5cbceaf2-c013-4f3a-94d4-1fa75b8a7525.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Multi-Resolution Continuous Normalizing Flows","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"annals-of-mathematics-and-artificial-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"amai","sideBox":"Learn more about [Annals of Mathematics and Artificial Intelligence](https://www.springer.com/journal/10472)","snPcode":"10472","submissionUrl":"https://submission.springernature.com/new-submission/10472/3","title":"Annals of Mathematics and Artificial Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Continuous Normalizing Flows, Image generation, wavelet","lastPublishedDoi":"10.21203/rs.3.rs-3027011/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3027011/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Recent work has shown that Neural Ordinary Differential Equations (ODEs) can serve as generative models of images using the perspective of Continuous Normalizing Flows (CNFs). 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