This paper studies structured node classification on graphs, where the predictions should consider dependencies between the node labels. In particular, we focus on solving the problem for partially labeled graphs where it is essential to incorporate the information in the known label for predicting the unknown labels. To address this issue, we propose a novel framework leveraging the diffusion probabilistic model for structured node classification (DPM-SNC). At the heart of our framework is the extraordinary capability of DPM-SNC to (a) learn a joint distribution over the labels with an expressive reverse diffusion process and (b) make predictions conditioned on the known labels utilizing manifold-constrained sampling. Since the DPMs lack training algorithms for partially labeled data, we design a novel training algorithm to apply DPMs, maximizing a new variational lower bound. We also theoretically analyze how DPMs benefit node classification by enhancing the expressive power of GNNs based on proposing AGG-WL, which is strictly more powerful than the classic 1-WL test. We extensively verify the superiority of our DPM-SNC in diverse scenarios, which include not only the transductive setting on partially labeled graphs but also the inductive setting and unlabeled graphs.

翻译：本文研究图上的结构化节点分类问题，其中预测应考虑节点标签之间的依赖关系。我们特别关注解决部分标注图上的问题，在这些图中，必须整合已知标签中的信息来预测未知标签。针对这一挑战，我们提出了一种利用扩散概率模型进行结构化节点分类的新框架（DPM-SNC）。该框架的核心在于DPM-SNC具有非凡的能力：（a）通过表达性反向扩散过程学习标签上的联合分布，以及（b）利用流形约束采样，基于已知标签进行条件预测。由于DPM缺乏针对部分标注数据的训练算法，我们设计了一种新的训练算法来应用DPM，最大化一个新的变分下界。我们还从理论上分析了DPM如何通过增强图神经网络的表达能力来提升节点分类性能，这基于我们提出的AGG-WL方法，其表达能力严格优于经典的1-WL测试。我们在多种场景下全面验证了DPM-SNC的优越性，这些场景不仅包括部分标注图上的转导式设置，还涵盖归纳式设置和无标注图。