Learning Mural Restoration from Degraded Data via Unsupervised Low-rank Residual Diffusion

Learning Mural Restoration from Degraded Data via Unsupervised Low-rank Residual Diffusion | 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 Article Learning Mural Restoration from Degraded Data via Unsupervised Low-rank Residual Diffusion Yao Yan, Zhengyan Lv, Chao Jiang, Zhengyun Cheng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8852475/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 14 You are reading this latest preprint version Abstract Ancient murals are invaluable cultural heritage artifacts that frequently suffer from complex degradation due to environmental exposure and human activity. Most existing computational restoration methods rely on supervised learning and require large collections of clean reference murals, which are often unavailable or prohibitively expensive to acquire. To address this challenge, we propose the first unsupervised mural restoration method based on residual diffusion. Our approach operates solely on degraded murals and corresponding simulated degradation noise, both of which can be obtained without ground-truth supervision. Rather than directly reconstructing the original clean image, we simulate additional degradation on already-damaged murals and train the model to invert this process through residual-aware diffusion. Furthermore, we incorporate a low-rank prior during sampling to promote global structural consistency. Extensive experiments demonstrate that our method achieves performance on par with or superior to state-of-the-art supervised techniques, establishing the viability of unsupervised learning for high-quality mural restoration. Mural Restoration Diffusion Unsupervised Low-rank Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 15 Mar, 2026 Reviews received at journal 12 Mar, 2026 Reviews received at journal 12 Mar, 2026 Reviews received at journal 11 Mar, 2026 Reviews received at journal 22 Feb, 2026 Reviewers agreed at journal 20 Feb, 2026 Reviewers agreed at journal 19 Feb, 2026 Reviewers agreed at journal 19 Feb, 2026 Reviewers agreed at journal 19 Feb, 2026 Reviewers agreed at journal 19 Feb, 2026 Reviewers invited by journal 19 Feb, 2026 Editor assigned by journal 17 Feb, 2026 Submission checks completed at journal 17 Feb, 2026 First submitted to journal 11 Feb, 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. 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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-8852475","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":595064702,"identity":"b94172da-66aa-452d-8675-2affed9947e5","order_by":0,"name":"Yao Yan","email":"","orcid":"","institution":"Xi’an Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Yao","middleName":"","lastName":"Yan","suffix":""},{"id":595064715,"identity":"d87cb1c6-95fd-4878-9111-c58066fcc011","order_by":1,"name":"Zhengyan Lv","email":"","orcid":"","institution":"Xi’an Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Zhengyan","middleName":"","lastName":"Lv","suffix":""},{"id":595064723,"identity":"2f597193-6ac0-4686-ae0a-009d76e9173b","order_by":2,"name":"Chao Jiang","email":"","orcid":"","institution":"Anhui University of Finance and Economics","correspondingAuthor":false,"prefix":"","firstName":"Chao","middleName":"","lastName":"Jiang","suffix":""},{"id":595064724,"identity":"cf0115e1-f129-4c5c-a587-b52e9ad897ff","order_by":3,"name":"Zhengyun Cheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYDACCQglx8DA2HgATRC/FmOglgbStCQ2AAnitPDPbj728Mufw+lr2w83HGDccTjP4ADzwds8DHZ5OC25cyzdWIbncO62M4lALWcOFxscYEu25mFILsalxUAix0xaQgKo5QBIS9vtxA0HeMykeRgOgJ2KXUv+N2kJg8PpZucfwrTwfyOgJYdN8kPC4QSzGwhb2PBqkbiRZibNcCDdcNsNoC2Jbf+LJQ+zGVvOMUjGqYV/RvIzyR9/rOXNzqc/fPCxLS2P73jzwxtvKuxwagEBZh6GZggrAYSYwQ7Gox4IGH8w1ME5CfjVjoJRMApGwUgEAIHuX+Nafy8kAAAAAElFTkSuQmCC","orcid":"","institution":"Northwestern Polytechnical University","correspondingAuthor":true,"prefix":"","firstName":"Zhengyun","middleName":"","lastName":"Cheng","suffix":""}],"badges":[],"createdAt":"2026-02-11 13:53:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8852475/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8852475/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103506547,"identity":"735bebd0-d879-4b4d-af68-c1603f5c1ee6","added_by":"auto","created_at":"2026-02-26 13:37:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7295208,"visible":true,"origin":"","legend":"","description":"","filename":"latex.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8852475/v1_covered_e0c5cf45-dfc7-4ca8-8050-323c7bcab4e8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Learning Mural Restoration from Degraded Data via Unsupervised Low-rank Residual Diffusion","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":"npj-heritage-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"hsci","sideBox":"Learn more about [Heritage Science](http://heritagesciencejournal.springeropen.com)","snPcode":"40494","submissionUrl":"https://submission.nature.com/new-submission/40494/3","title":"npj Heritage Science","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Mural Restoration, Diffusion, Unsupervised, Low-rank","lastPublishedDoi":"10.21203/rs.3.rs-8852475/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8852475/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\nAncient murals are invaluable cultural heritage artifacts that frequently suffer from complex degradation due to environmental exposure and human activity. Most existing computational restoration methods rely on supervised learning and require large collections of clean reference murals, which are often unavailable or prohibitively expensive to acquire. To address this challenge, we propose the first unsupervised mural restoration method based on residual diffusion. Our approach operates solely on degraded murals and corresponding simulated degradation noise, both of which can be obtained without ground-truth supervision. Rather than directly reconstructing the original clean image, we simulate additional degradation on already-damaged murals and train the model to invert this process through residual-aware diffusion. Furthermore, we incorporate a low-rank prior during sampling to promote global structural consistency. 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