Unfaithful text generation is a common problem for text generation systems. In the case of Data-to-Text (D2T) systems, the factuality of the generated text is particularly crucial for any real-world applications. We introduce R2D2, a training framework that addresses unfaithful Data-to-Text generation by training a system both as a generator and a faithfulness discriminator with additional replacement detection and unlikelihood learning tasks. To facilitate such training, we propose two methods for sampling unfaithful sentences. We argue that the poor entity retrieval capability of D2T systems is one of the primary sources of unfaithfulness, so in addition to the existing metrics, we further propose named entity based metrics to evaluate the fidelity of D2T generations. Our experimental results show that R2D2 systems could effectively mitigate the unfaithful text generation, and they achieve new state-of-theart results on FeTaQA, LogicNLG, and ToTTo, all with significant improvements.