In many real-world applications, such as image retrieval, it would be natural to measure the distances from one instance to others using \textit{instance specific distance} which captures the distinctions from the perspective of the concerned instance. However, there is no complete framework for learning instance specific distances since existing methods are incapable of learning such distances for test instance and unlabeled data. In this paper, we propose the ISD method to address this issue. The key of ISD is \textit{metric propagation}, that is, propagating and adapting metrics of individual labeled examples to individual unlabeled instances. We formulate the problem into a convex optimization framework and derive efficient solutions. Experiments show that ISD can effectively learn instance specific distances for labeled as well as unlabeled instances. The metric propagation scheme can also be used in other scenarios.