Previous question-answer pair generation methods aimed to produce fluent and meaningful question-answer pairs but tend to have poor diversity. Recent attempts addressing this issue suffer from either low model capacity or overcomplicated architecture. Furthermore, they overlooked the problem where the controllability of their models is highly dependent on the input. In this paper, we propose a model named VOLTA that enhances generative diversity by leveraging the Variational Autoencoder framework with a shared backbone network as its encoder and decoder. In addition, we propose adding InfoGAN-style latent codes to enable input-independent controllability over the generation process. We perform comprehensive experiments and the results show that our approach can significantly improve diversity and controllability over state-of-the-art models.