Flow-Adaptive Neural Processes with multiscale Spatial Bias for Irregular Inputs

Learning expressive function generation from irregular observations is challenging. Irregular observations can be random in available locations, order, and receiving numbers. To handle this problem, we introduce the Structured Flow Process (SFP), a novel generative neural process specifically designed to learn function priors through flow matching over finite-dimensional marginals and achieve efficient posterior inference. Our key innovation is Flow-adaptive Multihead Attention, which introduces multiscale spatial bias and flow-time conditioning into the velocity model to capture evolving correlations along the generative flow. SFP supports both prior modeling and posterior inference on irregular input sets and preserves the desired permutation invariance of the induced distributions. Empirically, SFP achieves strong performance across diverse prior-learning and posterior-inference tasks among synthetic stochastic processes, physical dynamical systems, and real geophysical fields. We further evaluate SFP on downstream applications, including tabular regression and Bayesian optimization with inputs of up to seven dimensions, demonstrating its scalability and broader applicability.