Our paper tackles the task of learning to generate signals over triangle meshes in a triangulation-agnostic manner, meaning the trained model can be applied to different mesh triangulations effectively. It proposes a specific noise distribution which is triangulation agnostic on meshes, to be used inside the Flow Matching's denoising process.</p>\n","updatedAt":"2026-05-20T17:23:03.820Z","author":{"_id":"6388484c3811d7ebe6e747fd","avatarUrl":"/avatars/ba9e9212f7b29adea2aaa162b2390911.svg","fullname":"Tianshu Kuai","name":"tkuai","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"isUserFollowing":false}},"numEdits":1,"identifiedLanguage":{"language":"en","probability":0.8159012198448181},"editors":["tkuai"],"editorAvatarUrls":["/avatars/ba9e9212f7b29adea2aaa162b2390911.svg"],"reactions":[],"isReport":false}}],"primaryEmailConfirmed":false,"paper":{"id":"2605.19305","authors":[{"_id":"6a0d7dd00cc88a0d483d3771","user":{"_id":"6388484c3811d7ebe6e747fd","avatarUrl":"/avatars/ba9e9212f7b29adea2aaa162b2390911.svg","isPro":false,"fullname":"Tianshu Kuai","user":"tkuai","type":"user","name":"tkuai"},"name":"Tianshu Kuai","status":"claimed_verified","statusLastChangedAt":"2026-05-20T17:09:48.605Z","hidden":false},{"_id":"6a0d7dd00cc88a0d483d3772","name":"Arman Maesumi","hidden":false},{"_id":"6a0d7dd00cc88a0d483d3773","name":"Daniel Ritchie","hidden":false},{"_id":"6a0d7dd00cc88a0d483d3774","name":"Noam Aigerman","hidden":false}],"publishedAt":"2026-05-19T00:00:00.000Z","submittedOnDailyAt":"2026-05-20T00:00:00.000Z","title":"Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes","submittedOnDailyBy":{"_id":"6388484c3811d7ebe6e747fd","avatarUrl":"/avatars/ba9e9212f7b29adea2aaa162b2390911.svg","isPro":false,"fullname":"Tianshu Kuai","user":"tkuai","type":"user","name":"tkuai"},"summary":"This paper tackles the task of learning to generate signals over triangle meshes in a triangulation-agnostic manner, meaning the trained model can be applied to different meshes and triangulations effectively. Practically, the paper adapts the flow matching (FM) paradigm to a mesh-based, triangulation-agnostic setting. Theoretically, it proposes a specific noise distribution which is triangulation agnostic, to be used inside the FM model's denoising process. While noise distributions are usually trivial to devise for, e.g., images, devising a triangulation-agnostic distribution proves to be a much more difficult task. We formulate a mathematical definition of triangulation agnosticism of distributions, via their spectrum. We then show that a discretization of a specific Gaussian random field called a Matérn process holds these desired properties, and provides a simple and efficient sampling algorithm. We use it as our noise model, and adapt FM to the triangulation-agnostic setting by using a state-of-the-art approach for learning signals on meshes in the gradient domain -- PoissonNet -- as the denoiser. We conduct experiments on elaborate tasks such as sampling elastic rest states, and generating poses of humanoids. Our method is shown to be capable of producing highly realistic results for meshes of over one million triangles, significantly exceeding the state-of-the-art in quality and diversity.","upvotes":2,"discussionId":"6a0d7dd10cc88a0d483d3775","projectPage":"https://matern-fm.github.io/","githubRepo":"https://github.com/kts707/matern-fm","githubRepoAddedBy":"user","ai_summary":"Flow matching is adapted to mesh-based signal generation through a triangulation-agnostic noise distribution based on Matérn processes and PoissonNet denoising.","ai_keywords":["flow matching","triangulation-agnostic","noise distribution","Gaussian random field","Matérn process","PoissonNet","denoising process","gradient domain","elastic rest states","humanoid poses"],"githubStars":2},"canReadDatabase":false,"canManagePapers":false,"canSubmit":false,"hasHfLevelAccess":false,"upvoted":false,"upvoters":[{"_id":"6388484c3811d7ebe6e747fd","avatarUrl":"/avatars/ba9e9212f7b29adea2aaa162b2390911.svg","isPro":false,"fullname":"Tianshu Kuai","user":"tkuai","type":"user"},{"_id":"6351e5bb3734c6e8a5c1bec1","avatarUrl":"/avatars/a784a51b369b197398575c3afbd5ceab.svg","isPro":false,"fullname":"Han-Bit Kang","user":"hbkang","type":"user"}],"acceptLanguages":["en"],"dailyPaperRank":0}">

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