We study the problem of training personalized deep learning models in a decentralized peer-to-peer setting, focusing on the setting where data distributions differ between the clients and where different clients have different local learning tasks. We study both covariate and label shift, and our contribution is an algorithm which for each client finds beneficial collaborations based on a similarity estimate for the local task. Our method does not rely on hyperparameters which are hard to estimate, such as the number of client clusters, but rather continuously adapts to the network topology using soft cluster assignment based on a novel adaptive gossip algorithm. We test the proposed method in various settings where data is not independent and identically distributed among the clients. The experimental evaluation shows that the proposed method performs better than previous state-of-the-art algorithms for this problem setting, and handles situations well where previous methods fail