Real-world data generation often involves certain geometries (e.g., graphs)
that induce instance-level interdependence. This characteristic makes the
generalization of learning models more difficult due to the intricate
interdependent patterns that impact data-generative distributions and can vary
from training to testing. In this work, we propose a geometric diffusion model
with learnable divergence fields for the challenging generalization problem
with interdependent data. We generalize the diffusion equation with stochastic
diffusivity at each time step, which aims to capture the multi-faceted
information flows among interdependent data. Furthermore, we derive a new
learning objective through causal inference, which can guide the model to learn
generalizable patterns of interdependence that are insensitive across domains.
Regarding practical implementation, we introduce three model instantiations
that can be considered as the generalized versions of GCN, GAT, and
Transformers, respectively, which possess advanced robustness against
distribution shifts. We demonstrate their promising efficacy for
out-of-distribution generalization on diverse real-world datasets.

我们提出了一个可学习的发散场几何扩散模型来解决依赖关系数据的挑战性泛化问题。通过引入随机扩散性来广义扩散方程，旨在捕捉依赖关系数据之间的多方面信息流动。另外，通过因果推断导出了一种新的学习目标，可指导模型学习对不同领域中都无关的依赖关系模式。在实际实现方面，我们提出了三种模型实例化方法，分别被视为 GCN、GAT 和 Transformers 的广义版本，具有对分布偏移的高鲁棒性。我们在不同的真实数据集上展示了这些模型在超出分布的泛化上的有希望的有效性。