Independence assumptions during sequence generation can speed up inference, but parallel generation of highly inter-dependent tokens comes at a cost in quality. Instead of assuming independence between neighbouring tokens (semi-autoregressive decoding, SA), we take inspiration from bidirectional sequence generation and introduce a decoder that generates target words from the left-to-right and right-to-left directions simultaneously. We show that we can easily convert a standard architecture for unidirectional decoding into a bidirectional decoder by simply interleaving the two directions and adapting the word positions and selfattention masks. Our interleaved bidirectional decoder (IBDecoder) retains the model simplicity and training efficiency of the standard Transformer, and on five machine translation tasks and two document summarization tasks, achieves a decoding speedup of ~2x compared to autoregressive decoding with comparable quality. Notably, it outperforms left-to-right SA because the independence assumptions in IBDecoder are more felicitous. To achieve even higher speedups, we explore hybrid models where we either simultaneously predict multiple neighbouring tokens per direction, or perform multi-directional decoding by partitioning the target sequence. These methods achieve speedups to 4x–11x across different tasks at the cost of <1 BLEU or <0.5 ROUGE (on average).