The task of multimodal relation extraction has attracted significant research attention, but progress is constrained by the scarcity of available training data. One natural thought is to extend existing datasets with cross-modal generative models. In this paper, we consider a novel problem setting, where only unimodal data, either text or image, are available during training. We aim to train a multimodal classifier from synthetic data that perform well on real multimodal test data. However, training with synthetic data suffers from two obstacles: lack of data diversity and label information loss. To alleviate the issues, we propose Mutual Information-aware Multimodal Iterated Relational dAta GEneration (MI2RAGE), which applies Chained Cross-modal Generation (CCG) to promote diversity in the generated data and exploits a teacher network to select valuable training samples with high mutual information with the ground-truth labels. Comparing our method to direct training on synthetic data, we observed a significant improvement of 24.06% F1 with synthetic text and 26.42% F1 with synthetic images. Notably, our best model trained on completely synthetic images outperforms prior state-of-the-art models trained on real multimodal data by a margin of 3.76% in F1. Our codebase will be made available upon acceptance.