State-of-the-art abstractive summarization systems frequently hallucinate content that is not supported by the source document, mainly due to noise in the training dataset.Existing methods opt to drop the noisy samples or tokens from the training set entirely, reducing the effective training set size and creating an artificial propensity to copy words from the source. In this work, we propose a training objective for abstractive summarization based on rejection learning, in which the model learns whether or not to reject potentially noisy tokens. We further propose a regularized decoding objective that penalizes non-factual candidate summaries during inference by using the rejection probability learned during training.We show that our method considerably improves the factuality of generated summaries in automatic and human evaluations when compared to five baseline models, and that it does so while increasing the abstractiveness of the generated summaries.