Recent advances in open-domain dialogue systems rely on the success of neural models that are trained on large-scale data. However, collecting large-scale dialogue data is usually time-consuming and labor-intensive. To address this data dilemma, we propose a novel data augmentation method for training open-domain dialogue models by utilizing unpaired data. Specifically, a data-level distillation process is first proposed to construct augmented dialogues where both post and response are retrieved from the unpaired data. A ranking module is employed to filter out low-quality dialogues. Further, a model-level distillation process is employed to distill a teacher model trained on high-quality paired data to augmented dialogue pairs, thereby preventing dialogue models from being affected by the noise in the augmented data. Automatic and manual evaluation indicates that our method can produce high-quality dialogue pairs with diverse contents, and the proposed data-level and model-level dialogue distillation can improve the performance of competitive baselines.