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Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>\n                    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\n                    <jats:italic toggle=\"yes\">Mat\u00e9rn process<\/jats:italic>\n                    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\u2014PoissonNet\u2014as 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.\n                  <\/jats:p>","DOI":"10.1145\/3811309","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Mat\u00e9rn Noise for Triangulation-Agnostic Flow Matching on Meshes"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-9880-1293","authenticated-orcid":false,"given":"Tianshu","family":"Kuai","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Montr\u00e9al, Montreal, Canada"},{"name":"Mila, Montreal, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7898-8061","authenticated-orcid":false,"given":"Arman","family":"Maesumi","sequence":"additional","affiliation":[{"name":"Brown University, Providence, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8253-0069","authenticated-orcid":false,"given":"Daniel","family":"Ritchie","sequence":"additional","affiliation":[{"name":"Brown University, Providence, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9116-4662","authenticated-orcid":false,"given":"Noam","family":"Aigerman","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Montr\u00e9al, Montreal, Canada"},{"name":"Mila, Montreal, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"International conference on machine learning. 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