We introduce EM-Network, a novel self-distillation approach that effectively leverages target information for supervised sequence-to-sequence (seq2seq) learning. In contrast to conventional methods, it is trained with oracle guidance, which is derived from the target sequence. Since the oracle guidance compactly represents the target-side context that can assist the sequence model in solving the task, the EM-Network achieves a better prediction compared to using only the source input. To allow the sequence model to inherit the promising capability of the EM-Network, we propose a new self-distillation strategy, where the original sequence model can benefit from the knowledge of the EM-Network in a one-stage manner. We conduct comprehensive experiments on two types of seq2seq models: connectionist temporal classification (CTC) for speech recognition and attention-based encoder-decoder (AED) for machine translation. Experimental results demonstrate that the EM-Network significantly advances the current state-of-the-art approaches, improving over the best prior work on speech recognition and establishing state-of-the-art performance on WMT'14 and IWSLT'14.