Reproduce “Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes” on OpenResearch
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About this paper
Tianshu Kuai, Arman Maesumi, Daniel Ritchie, Noam Aigerman
The authors introduce a mesh deformation generator that uses triangulation-agnostic Matérn noise, defined through the mesh Laplacian spectrum, to initialize a flow-matching process with a PoissonNet denoiser. In a MOYO/SMPL yoga-pose ablation, it lowers MSE × 10⁴ from 2.52 to 0.27 and improves MMD and coverage over naïve iid vertex noise. This result is specific to that comparison and task.
Key insights
- Triangulation agnosticism for distributions of signals on meshes can be formally defined and achieved by ensuring per-frequency independence, mesh-invariant frequency statistics, and bounded high-frequency content in the spectral domain.
- Matérn processes inherently satisfy the properties required for a triangulation-agnostic noise distribution, as their spectral characteristics (defined by a stochastic PDE) are consistent regardless of the underlying mesh discretization.
- Combining a theoretically grounded, triangulation-agnostic noise model with a robust, geometry-aware neural network architecture enables efficient training on lower-resolution meshes while maintaining performance for inference on diverse, high-resolution discretizations.
Summary by alphaXiv.
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