Label Distribution Learning (LDL) has been commonly studied in computer visionand many other IID data applications, due to its more generic setting than single-label and multi-label classification. This paper advances LDL into graph domainsand aims to tackle a novel heterogeneous graph label distribution learning (HGDL)problem. We argue that the graph heterogeneity reflected on node types, nodeattributes, and neighborhood structures can impose significant challenges for gen-eralizing LDL onto graphs. To address the challenges, we propose a new learningframework with two key components: 1) proactive graph topology homogenization,and 2) topology and content consistency-aware graph transformer. Specifically,the former learns optimal information aggregation between meta-paths, so that thenode heterogeneity can be proactively addressed prior to the succeeding embeddinglearning; the latter uses transformer-like architecture to learn consistency betweenmeta-path and node attributes, allowing network topology and nodal attributes to beequally emphasized during the label distribution learning. By using KL-divergenceand additional constraints, HGDL delivers an end-to-end solution for learning andpredicting label distribution for nodes. Both theoretical and empirical studiessubstantiate the effectiveness of our HGDL approach. Our code and datasets areavailable at https://anonymous.4open.science/r/HGDL-D014.