Graph Neural Diffusion as the Prior for In-Context Node Classification

Prior-fitted networks (PFNs) are pretrained on synthetic tasks sampled from a prior and make predictions on a new dataset in a single forward pass. Recently, PFN-based node classifiers have emerged as competitive models that classify the nodes of a new graph without training on it. For such models, the prior determines how the graph structure shapes the node features, and thus what the network can learn about graphs. However, the priors of existing PFN-based node classifiers either generate the features independently of the graph or only aggregate them over neighbours, and therefore produce a narrow range of the relations between features and graph structure found in real graphs. Graph neural diffusion views message passing as the integration of a diffusion equation on the graph, and subsequent work has proposed a variety of propagation schemes by adding terms such as reaction and advection. In this work, we propose GadrPFN, a PFN for node classification whose prior generates each task through graph neural diffusion. In each task, a node state on a random graph evolves under an advection–diffusion–reaction equation for a randomly drawn time, so that diffusion smooths the state along the edges and reaction sharpens it against them, and the node features are read from this state. GadrPFN is trained from scratch on about half a million synthetic tasks in two hours on a single GPU, whereas the strongest in-context node classifiers build on tabular foundation models pretrained on far more data. On 28 benchmarks, GadrPFN achieves the best mean accuracy and average rank on both homophilous and heterophilous graphs.