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PolarFlow, a continuous geometric flow-matching framework based on polar decomposition and truncated spectral coordinates, achieves generative quality comparable to competitive discrete methods while substantially reducing training and sampling time.
A subgraph filter algebra based on distance-aware Laplacian constructions is developed, defining a structured and controllable class of filters for effective approximation and quantifying how well the learned operator approximates the restricted ambient mapping.
By modeling the graph structure as a distribution conditioned on signal realizations, this framework provides a principled approach to signal-dependent graph structures, which are common in real-world applications, while explicitly encoding uncertainty in graph topology.
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