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Deep convolutional neural networks for image segmentation do not learn the label structure explicitly and may produce segmentations with an incorrect structure, e.g., with disconnected cylindrical structures in the segmentation of tree-like structures such as airways or blood vessels. In this paper, we propose a novel label refinement method to correct such errors from an initial segmentation, implicitly incorporating information about label structure. This method features two novel parts: 1) a model that generates synthetic structural errors, and 2) a label appearance simulation network that produces synthetic segmentations (with errors) that are similar in appearance to the real initial segmentations. Using these synthetic segmentations and the original images, the label refinement network is trained to correct errors and improve the initial segmentations. The proposed method is validated on two segmentation tasks: airway segmentation from chest computed tomography (CT) scans and brain vessel segmentation from 3D CT angiography (CTA) images of the brain. In both applications, our method significantly outperformed a standard 3D U-Net and other previous refinement approaches. Improvements are even larger when additional unlabeled data is used for model training. In an ablation study, we demonstrate the value of the different components of the proposed method.