Pseudo relevance feedback (PRF), which has been widely applied in IR, aims to derive a distribution from the top n pseudo relevant documents D. However, these documents are often a mixture of relevant and irrelevant documents. As a result, the derived distribution is actually a mixture model, which has long been limiting the performance of PRF. This is particularly the case when we deal with difficult queries where the truly relevant documents in D are very sparse. In this situation, it is often easier to identify a small number of seed irrelevant documents, which can form a seed irrelevant distribution. Then, a fundamental and challenging problem arises: solely based on the mixed distribution and a seed irrelevance distribution, how to automatically generate an optimal approximation of the true relevance distribution? In this paper, we propose a novel distribution separation model (DSM) to tackle this problem. Theoretical justifications of the proposed algorithm are given. Evaluatio...