Abstract: Distilling knowledge from a high-resource task, e.g., machine translation, is an effective way to alleviate the data scarcity problem of end-to-end speech translation. However, previous works simply use the classical knowledge distillation that does not allow for adequate transfer of knowledge from machine translation. In this paper, we propose a comprehensive knowledge distillation framework for speech translation, CKDST, which is capable of comprehensively and effectively distilling knowledge from machine translation to speech translation from two perspectives: cross-modal contrastive representation distillation and simultaneous decoupled knowledge distillation. In the former, we leverage a contrastive learning objective to optmize the mutual information between speech and text representations for representation distillation in the encoder. In the later, we decouple the non-target class knowledge from target class knowledge for logits distillation in the decoder. Experiments on the MuST-C benchmark dataset demonstrate that our CKDST substantially improves the baseline by 1.2 BLEU on average in all translation directions, and outperforms previous state-of-the-art end-to-end and cascaded speech translation models.