Title: A multi-task U-net for segmentation with lazy labels. Abstract: The need for labour intensive pixel-wise annotation is a major limitation of many fully supervised learning methods for image segmentation.   In this paper,  we propose a deep convolutional neural network for multi-class segmentation that circumvents this problem by being trainable on coarse data labels combined with only a very small number of images with pixel-wise annotations.  We call this new labelling strategy ‘lazy’ labels.  Image segmentation is then stratified into three connected tasks: rough detection of class instances, separation of wrongly connected objects without a clear boundary, and pixel-wise segmentation to find the accurate boundaries of each object. These problems are integrated into a multi-task learning framework and the model is trained end-to-end in a semi-supervised fashion. The method is demonstrated on two segmentation datasets, including food microscopy images and histology images of tissues respectively. We show that the model gives accurate segmentation results even if exact boundary labels are missing for a majority of the annotated data.  This allows more flexibility and efficiency for training deep neural networks that are data hungry in a practical setting where manual annotation is expensive, by collecting more lazy (rough) annotations than precisely segmented images. 