Learning from multimodal data is an important research topic in machine learning, which has the potential to obtain better representations. In this work, we propose a novel approach to generative modeling of multimodal data based on generative adversarial networks. To learn a coherent multimodal generative model, we show that it is necessary to align different encoder distributions with the joint decoder distribution simultaneously. To this end, we construct a specific form of the discriminator to enable our model to utilize data efficiently, which can be trained constrastively. By taking advantage of contrastive learning through factorizing the discriminator, we train our model on unimodal data. We have conducted experiments on the benchmark datasets, whose promising results show that our proposed approach outperforms the-state-ofthe-art methods on a variety of metrics. The source code is publicly available at https://github.com/6b5d/mmali.