This paper explores the area of personalized recommendation based on large-scale implicit feedback, where only positive feedback is available. To tackle the difficulty arising from lack of negative samples, a novel latent factor model IFRM is proposed, to convert the recommendation task into adoption probability optimization problem. To further improve efficiency and scalability, a parallel version of IFRM named p-IFRM is presented. By randomly partitioning users and items into buckets and thus reconstructing update sequence, IFRM can be learnt in parallel. The study theoretically derives the model from Bayesian analysis and experimentally demonstrates its effectiveness and efficiency by implementing p-IFRM under MapReduce framework and conducting comprehensive experiments on real world large datasets. The experiment results show that the model improves recommendation quality and performs well in scalability.