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General movement assessment (GMA) of infant movement videos (IMVs) is an effective method for the early detection of cerebral palsy (CP) in infants. Automated body parsing is a crucial step towards computer-aided GMA, in which infant body parts are segmented and tracked over time for movement analysis. However, acquiring fully annotated data for video-based body parsing is particularly expensive due to the large number of frames in IMVs. In this paper, we propose a semi-supervised body parsing model, termed SiamParseNet (SPN), to jointly learn single frame body parsing and label propagation between frames in a semi-supervised fashion. The Siamese-structured SPN consists of a shared feature encoder, followed by two separate branches: one for intra-frame body parts segmentation, and one for inter-frame label propagation. The two branches are trained jointly, taking pairs of frames from the same videos as their input. An adaptive training process is proposed that alternates training modes between using input pairs of only labeled frames and using inputs of both labeled and unlabeled frames. During testing, we employ a multi-source inference mechanism, where the final result for a test frame is either obtained via the segmentation branch or via propagation from a nearby key frame. We conduct extensive experiments on a partially-labeled IMV dataset where SPN outperforms all prior arts, demonstrating the effectiveness of our proposed method.