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.