  In recent years, visual question answering (VQA) has become topical. The
premise of VQA's significance as a benchmark in AI, is that both the image and
textual question need to be well understood and mutually grounded in order to
infer the correct answer. However, current VQA models perhaps `understand' less
than initially hoped, and instead master the easier task of exploiting cues
given away in the question and biases in the answer distribution. In this paper
we propose the inverse problem of VQA (iVQA). The iVQA task is to generate a
question that corresponds to a given image and answer pair. We propose a
variational iVQA model that can generate diverse, grammatically correct and
content correlated questions that match the given answer. Based on this model,
we show that iVQA is an interesting benchmark for visuo-linguistic
understanding, and a more challenging alternative to VQA because an iVQA model
needs to understand the image better to be successful. As a second
contribution, we show how to use iVQA in a novel reinforcement learning
framework to diagnose any existing VQA model by way of exposing its belief set:
the set of question-answer pairs that the VQA model would predict true for a
given image. This provides a completely new window into what VQA models
`believe' about images. We show that existing VQA models have more erroneous
beliefs than previously thought, revealing their intrinsic weaknesses.
Suggestions are then made on how to address these weaknesses going forward.
