Traditional domain adaptation methods address the performance degradation of deep learning models in diagnostic tasks under varying working conditions, assuming that source data is available. With the increasing demand for data privacy protection, access to source data has become restricted, leading to the rise of source-free domain adaptation methods. However, without any labels in the target domain, the adaptation process and performance of the model may be unstable and impractical for real-world scenarios. To address these issues, a semi-supervised source-free domain adaptation method via diffusive label propagation (SSFDA-DLP) is proposed in this paper. With only one labeled target sample provided for each class, SSFDA-DLP can diffuse the label information to the unlabeled target data through repeated iterations of pre-training with labeled target data and annotating new target data that are adjacent to the labeled ones. Considering that label propagation may incorrectly annotate some unlabeled samples, and to make full use of the unlabeled target data, feature and probability spaces consistency regularization is utilized to further improve the performance of the pre-trained model. The effectiveness and superiority of our method in source-free domain adaptation diagnostic tasks were evaluated on four datasets, including bearings and gears.