Gland instance segmentation is an essential but challenging task in the diagnosis and treatment of adenocarcinoma. The existing models usually achieve gland instance segmentation through multi-task learning and boundary loss constraint. However, how to deal with the problems of gland adhesion and inaccurate boundary in segmenting the complex samples remains a challenge. In this work, we propose a displacement-field assisted graph energy transmitter (DFGET) framework to solve these problems. Specifically, a novel message passing manner based on anisotropic diffusion is developed to update the node features, which can distinguish the isomorphic graphs and improve the expressivity of graph nodes for complex samples. Using such graph framework, the gland semantic segmentation map and the displacement field (DF) of the graph nodes are estimated with two graph network branches. With the constraint of DF, a graph cluster module based on diffusion theory is presented to improve the intra-class feature consistency and inter-class feature discrepancy, as well as to separate the adherent glands from the semantic segmentation maps. Extensive comparison and ablation experiments on the GlaS dataset demonstrate the superiority of DFGET and effectiveness of the proposed anisotropic message passing manner and clustering method. Compared to the best comparative model, DFGET increases the object-Dice and object-F1 score by 2.5% and 3.4% respectively, while decreases the object-HD by 32.4%, achieving state-of-the-art performance.