This paper is concerned with the task of collaborative density estimation in the distributed multi-task setting. Major application scenarios include collaborative anomaly detection among distributed industrial assets owned by different companies competing with each other. Of critical importance here is to achieve two conflicting goals at once: data privacy and collaboration. To this end, we propose a new framework for collaborative dictionary learning. By using a mixture of the exponential family, we show that collaborative learning can be nicely separated into three steps: local updates, global consensus, and optimization. For the critical step of consensus building, we propose a new algorithm that does not rely on expensive encryption-based multi-party computation. Our theoretical and experimental analysis shows that our method is several orders of magnitude faster than the alternative.