Accurately identifying new therapeutic uses for drugs is essential to advancing pharmaceutical research and development. Graph inference techniques have shown great promise in predicting drug–disease associations, offering both high convergence accuracy and efficiency. However, most existing methods fail to sufficiently address the issue of numerous missing information in drug–disease association networks. Moreover, existing methods are often constrained by local or single-directional reasoning. To overcome these limitations, we propose a novel approach, truncated arctangent rank minimization and double-strategy neighborhood constraint graph inference (TARMDNGI), for drug–disease association prediction. First, we calculate Gaussian kernel and Laplace kernel similarities for both drugs and diseases, which are then integrated using nonlinear fusion techniques. We introduce a new matrix completion technique, referred to as TARM. TARM takes the adjacency matrix of drug–disease heterogeneous networks as the target matrix and enhances the robustness and formability of the edges of DDA networks by truncated arctangent rank minimization. Additionally, we propose a double-strategy neighborhood constrained graph inference method to predict drug–disease associations. This technique focuses on the neighboring nodes of drugs and diseases, filtering out potential noise from more distant nodes. Furthermore, the DNGI method employs both top-down and bottom-up strategies to infer associations using the entire drug–disease heterogeneous network. The synergy of the dual strategies can enhance the comprehensive processing of complex structures and cross-domain associations in heterogeneous graphs, ensuring that the rich information in the network is fully utilized. Experimental results consistently demonstrate that TARMDNGI outperforms state-of-the-art models across two drug–disease datasets, one lncRNA-disease dataset, and one microbe-disease dataset.