Semi-supervised medical image segmentation has shown promise in training models with limited labeled data. However, current dominant teacher-student based approaches can suffer from the confirmation bias. To address this challenge, we propose AD-MT, an alternate diverse teaching approach in a teacher-student framework. It involves a single student model and two non-trainable teacher models that are momentum-updated periodically and randomly in an alternate fashion. To mitigate the confirmation bias via the diverse supervision, the core of AD-MT lies in two proposed modules: the Random Periodic Alternate (RPA) Updating Module and the Conflict-Combating Module (CCM). The RPA schedules an alternating diverse updating process with complementary data batches, distinct data augmentation, and random switching periods to encourage diverse reasoning from different teaching perspectives. The CCM employs an entropy-based ensembling strategy to encourage the model to learn from both the consistent and conflicting predictions between the teachers. Experimental results demonstrate the effectiveness and superiority of AD-MT on the 2D and 3D medical segmentation benchmarks across various semi-supervised settings.