Asking questions about visual environments is a crucial way for intelligent agents to understand rich multi-faceted scenes, raising the importance of Visual Question Generation (VQG) systems. Apart from being grounded to the image, existing VQG systems can use textual constraints, such as expected answers or knowledge triplets, to generate focused questions. These constraints allow VQG systems to specify the question content or leverage external commonsense knowledge that can not be obtained from the image content only. However, generating focused questions using textual constraints while enforcing a high relevance to the image content remains a challenge, as VQG systems often ignore one or both forms of grounding. In this work, we propose Contrastive Visual Question Generation (ConVQG), a method using a dual contrastive objective to discriminate questions generated using both modalities from those based on a single one. Experiments on both knowledge-aware and standard VQG benchmarks demonstrate that ConVQG outperforms the state-of-the-art methods and generates image-grounded, text-guided, and knowledge-rich questions. Our human evaluation results also show preference for ConVQG questions compared to non-contrastive baselines.