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While Generative Adversarial Networks (GANs) are fundamental to many generative modelling applications, they suffer from numerous issues. In this work, we propose a principled framework to simultaneously mitigate two fundamental issues in GANs: catastrophic forgetting of the discriminator and mode collapse of the generator. We achieve this by employing for GANs a contrastive learning and mutual information maximization approach, and perform extensive analyses to understand sources of improvements. Our approach significantly stabilizes GAN training and improves GAN performance for image synthesis across five datasets under the same training and evaluation conditions against state-of-the-art works. In particular, compared to the state-of-the-art SSGAN, our approach does not suffer from poorer performance on image domains such as faces, and instead improves performance significantly. Our approach is simple to implement and practical: it involves only one auxiliary objective, has a low computational cost, and performs robustly across a wide range of training settings and datasets without any hyperparameter tuning. For reproducibility, our code is available in Mimicry: https://github.com/kwotsin/mimicry.