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Voxel-wise contrastive learning (VCL) is a prominent approach in semi-supervised medical image segmentation. Based on the initially generated pseudo-labels, VCL pulls voxels with the same pseudo-labels toward their prototypes while pushes those with different labels apart, thereby learns effective representations for the segmentation task. However, in multi-organ segmentation (MoS), the complex anatomical structures of certain organs often lead to many unreliable pseudo-labels. Directly applying VCL can introduce confirmation bias, resulting in poor segmentation performance. A common practice is to first transform these unreliable pseudo-labels into more reliable complementary ones, which represent classes that voxels are least likely to belong to, and then push voxels away from the prototypes of their complementary labels. However, we find that in this approach, if voxels with unreliable pseudo-labels are originally close in feature space, they can end up far apart after being pushed away from their complementary prototypes. This disruption of the semantic relationships among voxels can be detrimental to the MoS task. In this paper, we propose DVCL, a novel distance-aware VCL method for semi-supervised MoS. DVCL is based on the observation that voxels close to each other in the feature space ('neighbors') likely belong to the same semantic category, while distant ones ('outsiders') likely belong to different categories. In DVCL, we first identify neighbors and outsiders for all voxels with unreliable pseudo-labels, and then pull their neighbors into the same clusters while pushing outsiders away. In this way, neighbors of unreliable voxels remain their neighbors and outsiders remain outsiders. This approach helps maintain useful semantic relationships among unreliable voxels while still enjoying the advantages of VCL. We conduct extensive experiments on four datasets to validate the effectiveness. Extensive experiments on four datasets demonstrate the superior performance of DVCL compared to state-of-the-art methods.