Manually annotating accurate 3D hand poses is extremely time-consuming and labor-intensive. Existing self-supervised hand pose estimation methods leverage the discrepancy between input images and rendered outputs, or multi-view consistency constraints, as the driving force to optimize networks and progressively refine pose accuracy. However, these methods are highly susceptible to noisy pseudo-labels and overlook the importance of fully exploiting fine-grained spatial correlations, which undermines the stability of model training. To address these issues, we propose UST-Hand, a self-supervised learning framework that estimates uncertainty distribution of hand pose and constructs a probabilistic point cloud feature space, which enables the complex spatiotemporal relationship modeling. UST-Hand employs a conditional normalizing flow model to capture hand pose distributions and samples diverse hypotheses, facilitating robust learning under noisy pseudo-labels supervision with enhanced stability. These multi-hypothesis are mapped to a unified probabilistic 3D point cloud space for multi-view and temporal feature interaction, comprehensively exploring hand motion patterns and fine-grained spatial correlations. Extensive experiments on three challenging datasets demonstrate that UST-Hand achieves state-of-the-art performance, outperforming existing self-supervised methods by up to 37.8% in Mean Per Vertex Position Error (MPVPE).

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