In this work, we attempt the segmentation of cardiac structures in late gadolinium-enhanced (LGE) magnetic resonance images (MRI) using only minimal supervision in a two-step approach. In the first step, we register a small set of five LGE cardiac magnetic resonance (CMR) images with ground truth labels to a set of 40 target LGE CMR images without annotation. Each manually annotated ground truth provides labels of the myocardium and the left ventricle (LV) and right ventricle (RV) cavities, which are used as atlases. After multi-atlas label fusion by majority voting, we possess noisy labels for each of the targeted LGE images. A second set of manual labels exists for 30 patients of the target LGE CMR images, but are annotated on different MRI sequences (bSSFP and T2-weighted). Again, we use multi-atlas label fusion with a consistency constraint to further refine our noisy labels if additional annotations in other modalities are available for a given patient. In the second step, we train a deep convolutional network for semantic segmentation on the target data while using data augmentation techniques to avoid over-fitting to the noisy labels. After inference and simple post-processing, we achieve our final segmentation for the targeted LGE CMR images, resulting in an average Dice of 0.890, 0.780, and 0.844 for LV cavity, LV myocardium, and RV cavity, respectively.