arXiv Machine Learning September 30, 2026 By James Rowbottom, Elizabeth L. Baker, Nick Huang, Ben Adcock, Carola-Bibiane Sch\"onlieb, Alexander Denker

GRIFDIR: Graph Resolution-Invariant Diffusion Models over Irregular Domains

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GRIFDIR is a new architecture for score-based diffusion models that operates directly on unstructured meshes, enabling function-space diffusion over irregular domains. By representing generalized graph convolutional kernels as finite element functions, the model achieves resolution invariance and can handle complex, non-convex, and multiply-connected geometries. Experiments demonstrate that GRIFDIR maintains high fidelity in both unconditional and conditional sampling across diverse shapes.

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