Mitigating Lipschitz Singularities in Long-Tailed Diffusion Models via Time-Step Sharing Strategy

Mitigating Lipschitz Singularities in Long-Tailed Diffusion Models via Time-Step Sharing Strategy | 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 Mitigating Lipschitz Singularities in Long-Tailed Diffusion Models via Time-Step Sharing Strategy Qiangkui Leng, Zhuoyu Zhou, Keyi Song, Guansheng Yuan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7069918/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Dec, 2025 Read the published version in The Visual Computer → Version 1 posted 9 You are reading this latest preprint version Abstract Diffusion models have demonstrated remarkable success in generating diverse and high-fidelity images. However, their performance often degrades when applied to long-tailed datasets, where head classes significantly outnumber tail classes. This imbalance leads to biased model training, favoring head classes and neglecting tail classes. To address this challenge, we conduct an in-depth analysis of the Lipschitz singularity problem that arises near zero timesteps in long-tailed diffusion models, causing numerical instability and degraded image quality. We propose a time-step sharing based class-balancing diffusion model (TCDM) that effectively mitigates this issue by combining a shared timestep strategy with a conditional probability transfer mechanism. TCDM improves noise prediction accuracy and information transfer stability, leading to enhanced image generation quality for tail classes. Experimental results on multiple long-tailed datasets, including CIFAR-100LT and CIFAR-10LT, demonstrate TCDM's superior performance, achieving leading FID scores and higher recall rates compared to existing methods. Here, we show that TCDM significantly reduces the Lipschitz constant near zero, ensuring more stable and accurate noise prediction and feature transfer. This research contributes to the broader field of generative models by providing a robust solution for handling long-tailed distributions in image generation tasks. Our code is available at https://github.com/shiyanbei306/TCDM . Image generation Long-tailed distribution Diffusion model Lipschitz constant Sampler Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Dec, 2025 Read the published version in The Visual Computer → Version 1 posted Editorial decision: Revision requested 21 Aug, 2025 Reviews received at journal 12 Aug, 2025 Reviews received at journal 07 Aug, 2025 Reviewers agreed at journal 21 Jul, 2025 Reviewers agreed at journal 21 Jul, 2025 Reviewers invited by journal 14 Jul, 2025 Editor assigned by journal 08 Jul, 2025 Submission checks completed at journal 08 Jul, 2025 First submitted to journal 07 Jul, 2025 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-7069918","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":486035726,"identity":"c1db4e6f-d524-4d96-9d56-f22856cf7856","order_by":0,"name":"Qiangkui Leng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuUlEQVRIiWNgGAWjYDACHuYGIGnDw8/eQLQWRpDSNBnJngOkaTlsY3DDgUgdfGcONj4u+HWeh+EGA+OHjzlEaJE829hsPLPvNg/j7AZmyZnbiNBicJ6xTZq35zYPs8wBNmZeIrW0/+btOcfDJpFArJazjW3MPD8O8PAQrUXyzMFmad6GZB4JnoPNxPmF70zywc88f+zs7Y83H/zwkRgtDAeAmLENxAJHELFaGP4QqXgUjIJRMApGJgAAZp43782DVCQAAAAASUVORK5CYII=","orcid":"","institution":"Liaoning Technical University","correspondingAuthor":true,"prefix":"","firstName":"Qiangkui","middleName":"","lastName":"Leng","suffix":""},{"id":486035727,"identity":"5f7b6b74-238d-4811-8693-e3740ac50511","order_by":1,"name":"Zhuoyu Zhou","email":"","orcid":"","institution":"Liaoning Technical University","correspondingAuthor":false,"prefix":"","firstName":"Zhuoyu","middleName":"","lastName":"Zhou","suffix":""},{"id":486035728,"identity":"57581f1d-37c1-4587-8f3d-b39034e2873b","order_by":2,"name":"Keyi Song","email":"","orcid":"","institution":"Liaoning Technical University","correspondingAuthor":false,"prefix":"","firstName":"Keyi","middleName":"","lastName":"Song","suffix":""},{"id":486035729,"identity":"1b074609-8eb6-4483-b0b9-68db80cbb677","order_by":3,"name":"Guansheng Yuan","email":"","orcid":"","institution":"Liaoning Technical University","correspondingAuthor":false,"prefix":"","firstName":"Guansheng","middleName":"","lastName":"Yuan","suffix":""}],"badges":[],"createdAt":"2025-07-08 03:08:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7069918/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7069918/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00371-025-04312-x","type":"published","date":"2025-12-17T15:57:55+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98814085,"identity":"e2cec6ee-7d9d-49f1-abba-e9c6a1dd54f9","added_by":"auto","created_at":"2025-12-22 16:10:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":995249,"visible":true,"origin":"","legend":"","description":"","filename":"TCDM.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7069918/v1_covered_4c9b6b3e-dbaf-4a06-80af-fad68f683d81.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mitigating Lipschitz Singularities in Long-Tailed Diffusion Models via Time-Step Sharing Strategy","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":"the-visual-computer","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"tvcj","sideBox":"Learn more about [The Visual Computer](http://link.springer.com/journal/371)","snPcode":"371","submissionUrl":"https://submission.nature.com/new-submission/371/3","title":"The Visual Computer","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Image generation, Long-tailed distribution, Diffusion model, Lipschitz constant, Sampler","lastPublishedDoi":"10.21203/rs.3.rs-7069918/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7069918/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDiffusion models have demonstrated remarkable success in generating diverse and high-fidelity images. 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