The widespread success of deep learning models today is owed to the curation of extensive datasets significant in size and complexity. However, such models frequently pick up inherent biases in the data during the training process, leading to unreliable predictions. Diagnosing and debiasing datasets is thus a necessity to ensure reliable model performance. In this paper, we present ConBias, a novel framework for diagnosing and mitigating Concept co-occurrence Biases in visual datasets. ConBias represents visual datasets as knowledge graphs of concepts, enabling meticulous analysis of spurious concept co-occurrences to uncover concept imbalances across the whole dataset. Moreover, we show that by employing a novel clique-based concept balancing strategy, we can mitigate these imbalances, leading to enhanced performance on downstream tasks. Extensive experiments show that data augmentation based on a balanced concept distribution augmented by ConBias improves generalization performance across multiple datasets compared to state-of-the-art methods. We will make our code and data publicly available.