Abstract Semantic parsing aims to transform natural language (NL) utterances into formal meaning representations (MRs), whereas an NL generator achieves the reverse: producing a NL description for some given MRs. Despite this intrinsic connection, the two tasks are often studied separately in prior work. In this paper, we model the duality of these two tasks via a joint learning framework, and demonstrate its effectiveness of boosting the performance on both tasks. Concretely, we propose the method of dual information maximization (DIM) to regularize the learning process, where DIM empirically maximizes the variational lower bounds of expected joint distributions of NL and MRs. We further extend DIM to a semisupervision setup (SEMIDIM), which leverages unlabeled data of both tasks. Experiments on three datasets of dialogue management and code generation (and summarization) show that performance on both semantic parsing and NL generation can be consistently improved by DIM, in both supervised and semi-supervised setups1.