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Fully supervised change detection methods require difficult to procure pixel-level labels, while weakly supervised approaches can be trained with image-level labels. However, most of these approaches require a combination of changed and unchanged image pairs for training. Thus, these methods can not directly be used for datasets where only changed image pairs are available. We present W-CDNet, a novel weakly supervised change detection network that can be trained with image-level semantic labels. Additionally, W-CDNet can be trained with two different types of datasets, either containing changed image pairs only or a mixture of changed and unchanged image pairs. Since we use image-level semantic labels for training, we simultaneously create a change mask and label the changed object for single-label images. W-CDNet employs a W-shaped siamese U-net to extract feature maps from an image pair which then get compared in order to create a raw change mask. The core part of our model, the Change Segmentation and Classification (CSC) module, learns an accurate change mask at a hidden layer by using a custom Remapping Block and then segmenting the current input image with the change mask. The segmented image is used to predict the image-level semantic label. The correct label can only be predicted if the change mask actually marks relevant change. This forces the model to learn an accurate change mask. We demonstrate the segmentation and classification performance of our approach and achieve top results on AICD and HRSCD, two public aerial imaging change detection datasets as well as on a Food Waste change detection dataset. Our code is available at https://github.com/PhiAbs/W-CDNet .