Multi-label image recognition with partial labels (MLR-PL), in which some labels are known while others are unknown for each image, may greatly reduce the cost of annotation and thus facilitate large-scale MLR. We find that strong semantic correlations exist within each image and across different images, and these correlations can help transfer the knowledge possessed by the known labels to retrieve the unknown labels and thus improve the performance of the MLR-PL task. In this work, we propose a novel heterogeneous semantic transfer (HST) framework that consists of two complementary transfer modules that explore both within-image and cross-image semantic correlations to transfer the knowledge possessed by known labels to generate pseudo labels for the unknown labels. Specifically, an intra-image semantic transfer (IST) module learns an image-specific label co-occurrence matrix for each image and maps the known labels to complement the unknown labels based on these matrices. Additionally, a cross-image transfer (CST) module learns category-specific feature-prototype similarities and then helps complement the unknown labels that have high degrees of similarity with the corresponding prototypes. It is worthy-noting that the HST framework requires searching appropriate thresholds to determine the co-occurrence and similarity scores to generate pseudo labels for the IST and CST modules, respectively. To avoid highly time-consuming and resource-intensive manual tuning, we introduce a differential threshold learning algorithm that adjusts the nondifferential indication function to a differential formulation to automatically learn the appropriate thresholds. Finally, both the known and generated pseudo labels are used to train MLR models. Extensive experiments conducted on the Microsoft COCO, Visual Genome, and Pascal VOC 2007 datasets show that the proposed HST framework achieves superior performance to that of current state-of-the-art algorithms. Specifically, it obtains mean average precision (mAP) improvements of 1.4, 3.3, and 0.4% on the three datasets over the results of the best-performing previously developed algorithm.