The task of visual question generation (VQG) aims to generate human-like neural questions from an image and potentially other side information (e.g., answer type or the answer itself). Existing works often suffer from the severe one image to many questions mapping problem, which generates uninformative and non-referential questions. Recent work has demonstrated that by leveraging double visual and answer hints, a model can faithfully generate much better quality questions. However, visual hints are not available naturally. Despite they proposed a simple rule-based similarity matching method to obtain candidate visual hints, they could be very noisy practically and thus restrict the quality of generated questions. In this paper, we present a novel learning approach for double-hints based VQG, which can be cast as a weakly supervised learning problem with noises. The key rationale is that the salient visual regions of interest can be viewed as a constraint to improve the generation procedure for producing high-quality questions. As a result, given the predicted salient visual regions of interest, we can focus on estimating the probability of being ground-truth questions, which in turn implicitly measures the quality of predicted visual hints. Experimental results on two benchmark datasets show that our proposed method outperforms the state-of-the-art approaches by a large margin on a variety of metrics, including both automatic machine metrics and human evaluation.