Real-world data generation often involves certain geometries that induce the instance-level interdependence. This characteristic makes generalization of the model more difficult due to the intricate underlying manifolds that are nonnegligible for data modeling and can vary from training to testing. In this work, we propose a geometric diffusion model with branching-structured divergence fields for the challenging generalization problem with interdependent data. We generalize the diffusion equation with stochastic diffusivity functions at each time step which aims to capture the multi-faceted information flows among interdependent data. For optimization, we devise a step-wise re-weighting regularization approach that facilitates the model to learn stable predictive relations insensitive to domain context. We also introduce three model instantiations as practical implementation versions, and demonstrate their promising efficacy on datasets with diverse distribution shifts involving data geometries.