Abstract: In this paper, we introduce an unsupervised discourse constituency parsing algorithm. We use Viterbi EM with a margin-based criterion to train a span-based discourse parser in an unsupervised manner. We also propose initialization methods for Viterbi training of discourse constituents based on our prior knowledge of text structures. Experimental results demonstrate that our unsupervised parser achieves comparable or even superior performance to fully supervised parsers. We also investigate discourse constituents that are learned by our method.