Paper page - Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes

Source: https://huggingface.co/papers/2605.19305

Abstract

Flow matching is adapted to mesh-based signal generation through a triangulation-agnostic noise distribution based on Matérn processes and PoissonNet denoising.

This paper tackles the task of learning to generate signals over triangle meshes in atriangulation-agnosticmanner, meaning the trained model can be applied to different meshes and triangulations effectively. Practically, the paper adapts theflow matching(FM) paradigm to a mesh-based,triangulation-agnosticsetting. Theoretically, it proposes a specificnoise distributionwhich is triangulation agnostic, to be used inside the FM model’sdenoising process. Whilenoise distributions are usually trivial to devise for, e.g., images, devising atriangulation-agnosticdistribution 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 specificGaussian random fieldcalled aMatérn processholds these desired properties, and provides a simple and efficient sampling algorithm. We use it as our noise model, and adapt FM to thetriangulation-agnosticsetting by using a state-of-the-art approach for learning signals on meshes in thegradient domain--PoissonNet-- as the denoiser. We conduct experiments on elaborate tasks such as samplingelastic 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.

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