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Transfer learning has been successfully applied across many high-impact applications. However, most existing work focuses on the static transfer learning setting, and very little is devoted to modeling the time evolving target domain, such as the online reviews for movies. To bridge this gap, in this paper, we study a novel continuous transfer learning setting with a time evolving target domain. One major challenge associated with continuous transfer learning is the potential occurrence of negative transfer as the target domain evolves over time. To address this challenge, we propose a novel label-informed C-divergence between the source and target domains in order to measure the shift of data distributions as well as to identify potential negative transfer. We then derive the error bound for the target domain using the empirical estimate of our proposed C-divergence. Furthermore, we propose a generic adversarial Variational Auto-encoder framework named TransLATE by minimizing the classification error and C-divergence of the target domain between consecutive time stamps in a latent feature space. In addition, we define a transfer signature for characterizing the negative transfer based on C-divergence, which indicates that larger C-divergence implies a higher probability of negative transfer in real scenarios. Extensive experiments on synthetic and real data sets demonstrate the effectiveness of our TransLATE framework.