We present DADS, a novel Data Augmentation technique for low-resource Dialogue Summarization. Our method generates synthetic examples by replacing sections of text from both the input dialogue and summary while preserving the augmented summary to correspond to a viable summary for the augmented dialogue. We utilize pretrained language models that produce highly likely dialogue alternatives while still being free to generate diverse alternatives. We applied our data augmentation method to the SAMSum dataset in low resource scenarios, mimicking real world problems such as chat, thread, and meeting summarization where large scale supervised datasets with human-written summaries are scarce. Through both automatic and human evaluations, we show that DADS shows strong improvements for low resource scenarios while generating topically diverse summaries without introducing additional hallucinations to the summaries.