We introduce the problem of learning affective correspondence between audio (music) and visual data (images). For this task, a music clip and an image are considered similar (having true correspondence) if they have similar emotion content. In order to estimate this crossmodal, emotion-centric similarity, we propose a deep neural network architecture that learns to project the data from the two modalities to a common representation space, and performs a binary classification task of predicting the affective correspondence (true or false). To facilitate the current study, we construct a large scale database containing more than $3,500$ music clips and $85,000$ images with three emotion classes (positive, neutral, negative). The proposed approach achieves $61.67\%$ accuracy for the affective correspondence prediction task on this database, outperforming two relevant and competitive baselines. We also demonstrate that our network learns modality-specific representations of emotion (without explicitly being trained with emotion labels), which are useful for emotion recognition in individual modalities.