The Paraphrase Database (PPDB; Ganitkevitch et al., 2013) is an extensive semantic resource, consisting of a list of phrase pairs with (heuristic) confidence estimates. However, it is still unclear how it can best be used, due to the heuristic nature of the confidences and its necessarily incomplete coverage. We propose models to leverage the phrase pairs from the PPDB to build parametric paraphrase models that score paraphrase pairs more accurately than the PPDB's internal scores while simultaneously improving its coverage. They allow for learning phrase embeddings as well as improved word embeddings. Moreover, we introduce two new, manually annotated datasets to evaluate short-phrase paraphrasing models. Using our paraphrase model trained using PPDB, we achieve state-of-the-art results on standard word and bigram similarity tasks and beat strong baselines on our new short phrase paraphrase tasks.