Generative Adversarial Networks (GANs) are a class of generative models used for various applications, but they have been known to suffer from the mode collapse problem, in which some modes of the target distribution are ignored by the generator. Investigative study using a new data generation procedure indicates that the mode collapse of the generator is driven by the discriminator's inability to maintain classification accuracy on previously seen samples, a phenomenon called Catastrophic Forgetting in continual learning. Motivated by this observation, we introduce a novel training procedure that adaptively spawns additional discriminators to remember previous modes of generation. On several datasets, we show that our training scheme can be plugged-in to existing GAN frameworks to mitigate mode collapse and improve standard metrics for GAN evaluation.