Spatial data are ubiquitous and have transformed decision-making in many critical domains, including public health, agriculture, transportation, etc. While recent advances in machine learning offer promising ways to harness massive spatial datasets (e.g., satellite imagery), spatial heterogeneity -- a fundamental property of spatial data -- poses a major challenge as data distributions or generative processes often vary over space. Recent studies targeting this difficult problem either require a known space-partitioning as the input, or can only support limited special cases (e.g., binary classification). Moreover, heterogeneity-pattern learned by these methods are locked to the locations of the training samples, and cannot be applied to new locations. We propose a statistically-guided framework to adaptively partition data in space during training using distribution-driven optimization and transform a deep learning model (of user's choice) into a heterogeneity-aware architecture. We also propose a spatial moderator to generalize learned patterns to new test regions. Experiment results on real-world datasets show that the framework can effectively capture footprints of heterogeneity and substantially improve prediction performances.