Despite the impressive text-to-image (T2I) synthesis capabilities of diffusion models, they often struggle to understand compositional relationships between objects and attributes, especially in complex settings. Existing approaches through building compositional architectures or generating difficult negative captions often assume a fixed prespecified compositional structure, which limits generalization to new distributions. In this paper, we argue that curriculum training is crucial to equipping generative models with a fundamental understanding of compositionality. To achieve this, we leverage large-language models (LLMs) to automatically compose complex scenarios and harness Visual-Question Answering (VQA) checkers to automatically curate a contrastive dataset, ConPair, consisting of 15k pairs of high-quality contrastive images. These pairs feature minimal visual discrepancies and cover a wide range of attribute categories, especially complex and natural scenarios. To learn effectively from these error cases (i.e., hard negative images), we propose EvoGen, a new multi-stage curriculum for contrastive learning of diffusion models. Through extensive experiments across a wide range of compositional scenarios, we showcase the effectiveness of our proposed framework on compositional T2I benchmarks.