Image translation with convolutional neural networks has recently been used as an approach to multimodal change detection. Existing approaches train the networks by exploiting supervised information of the change areas, which, however, is not always available. A main challenge in the unsupervised problem setting is to avoid that change pixels affect the learning of the translation function. We propose two new network architectures trained with loss functions weighted by priors that reduce the impact of change pixels on the learning objective. The change prior is derived in an unsupervised fashion from relational pixel information captured by domain-specific affinity matrices. Specifically, we use the vertex degrees associated with an absolute affinity difference matrix and demonstrate their utility in combination with cycle consistency and adversarial training. The proposed neural networks are compared with state-of-the-art algorithms. Experiments conducted on two real datasets show the effectiveness of our methodology.