The task of knowledge base population (KBP) aims to discover facts about entities from texts and expand a knowledge base with these facts. Previous studies shape end-to-end KBP as a machine translation task, which is required to convert unordered fact into a sequence according to a pre-specified order. However, the facts stated in a sentence are unordered in essence. In this paper, we formulate end-to-end KBP as a direct set generation problem, avoiding considering the order of multiple facts. To solve the set generation problem, we propose networks featured by transformers with non-autoregressive parallel decoding. Unlike previous approaches that use an autoregressive decoder to generate facts one by one, the proposed networks can directly output the final set of facts in one shot. Furthermore, to train the networks, we also design a set-based loss that forces unique predictions via bipartite matching. Compared with cross-entropy loss that highly penalizes small shifts in fact order, the proposed bipartite matching loss is invariant to any permutation of predictions. Benefiting from getting rid of the burden of predicting the order of multiple facts, our proposed networks achieve state-of-the-art (SoTA) performance on two benchmark datasets.