Sequential learning of tasks using gradient descent leads to an unremitting decline in the accuracy of tasks for which training data is no longer available, termed catastrophic forgetting. Generative models have been explored as a means to approximate the distribution of old tasks and bypass storage of real data. Here we propose a cumulative closed-loop memory replay GAN (CloGAN) provided with external regularization by a small memory unit selected for maximum sample diversity. We evaluate incremental class learning using a notoriously hard paradigm, single-headed learning, in which each task is a disjoint subset of classes in the overall dataset, and performance is evaluated on all previous classes. First, we show that when constructing a dynamic memory unit to preserve sample heterogeneity, model performance asymptotically approaches training on the full dataset. We then show that using a stochastic generator to continuously output fresh new images during training increases performance significantly further meanwhile generating quality images. We compare our approach to several baselines including fine-tuning by gradient descent (FGD), Elastic Weight Consolidation (EWC), Deep Generative Replay (DGR) and Memory Replay GAN (MeRGAN). Our method has very low long-term memory cost, the memory unit, as well as negligible intermediate memory storage.