GeoFunFlow: Geometric function flow matching for joint probabilistic inference of physical fields and complex geometries
GeoFunFlow is a new geometric diffusion model that combines a geometry-aware autoencoder with a latent diffusion model to jointly infer physical fields over complex shapes from sparse data. It learns compact representations of fields and uses rectified flow dynamics to sample the true posterior distribution, achieving state-of-the-art reconstruction accuracy on challenging geometries.