Effective inference for a generative adversarial model remains an important and challenging problem. We propose a novel approach, Decomposed Adversarial Learned Inference (DALI), which explicitly matches prior and conditional distributions in both data and code spaces, and puts a direct constraint on the dependency structure of the generative model. We derive an equivalent form of the prior and conditional matching objective that can be optimized efficiently without any parametric assumption on the data. We validate the effectiveness of DALI on the MNIST, CIFAR-10, and CelebA datasets by conducting quantitative and qualitative evaluations. Results demonstrate that DALI significantly improves both reconstruction and generation as compared to other adversarial inference models.