Generating a set of text is a common challenge for many NLP applications, for example, automatically providing multiple keyphrases for a document to facilitate user reading. Existing generative models use a sequential decoder that generates a single sequence successively, and the set generation problem is converted to sequence generation via concatenating multiple text into a long text sequence. However, the elements of a set are unordered, which makes this scheme suffer from biased or conflicting training signals. In this paper, we propose a branching decoder, which can generate a dynamic number of tokens at each time-step and branch multiple generation paths. In particular, paths are generated individually so that no order dependence is required. Moreover, multiple paths can be generated in parallel which greatly reduces the inference time. Experiments on several keyphrase generation datasets demonstrate that the branching decoder is more effective and efficient than the existing sequential decoder.