In sequence to sequence generation tasks (e.g. machine translation and abstractive summarization), inference is generally performed in a left-to-right manner to produce the result token by token. The neural approaches, such as LSTM and self-attention networks, are now able to make full use of all the predicted history hypotheses from left side during inference, but cannot meanwhile access any future (right side) information and usually generate unbalanced outputs (e.g. left parts are much more accurate than right ones in Chinese-English translation). In this work, we propose a synchronous bidirectional inference model to generate outputs using both left-to-right and right-to-left decoding simultaneously and interactively. First, we introduce a novel beam search algorithm that facilitates synchronous bidirectional decoding. Then, we present the core approach which enables left-to-right and right-to-left decoding to interact with each other, so as to utilize both the history and future predictions simultaneously during inference. We apply the proposed model to both LSTM and self-attention networks. Furthermore, we propose a novel fine-tuning based parameter optimization algorithm in addition to the simple two-pass strategy. The extensive experiments on machine translation and abstractive summarization demonstrate that our synchronous bidirectional inference model can achieve remarkable improvements over the strong baselines.