Methods, systems, and apparatus, including computer programs encoded on computer storage media, for performing sequence modeling tasks using insertions. One of the methods includes receiving a system input that includes one or more source elements from a source sequence and zero or more target elements from a target sequence, wherein each source element is selected from a vocabulary of source elements and wherein each target element is selected from a vocabulary of target elements; generating a partial concatenated sequence that includes the one or more source elements from the source sequence and the zero or more target elements from the target sequence, wherein the source and target elements arranged in the partial concatenated sequence according to a combined order; and generating a final concatenated sequence that includes a finalized source sequence and a finalized target sequence, wherein the finalized target sequence includes one or more target elements.