Abstract We extend a pair of continuous combinator-based constituency parsers (one binary and one multi-branching) into a discontinuous pair. Our parsers iteratively compose constituent vectors from word embeddings without any grammar constraints. Their empirical complexities are subquadratic. Our extension includes 1) a swap action for the orientation-based binary model and 2) biaffine attention for the chunker-based multi-branching model. In tests conducted with the Discontinuous Penn Treebank and TIGER Treebank, we achieved state-of-the-art discontinuous accuracy with a significant speed advantage.