We present a continual learning approach for generative adversarial networks\n(GANs), by designing and leveraging parameter-efficient feature map\ntransformations. Our approach is based on learning a set of global and\ntask-specific parameters. The global parameters are fixed across tasks whereas\nthe task-specific parameters act as local adapters for each task, and help in\nefficiently obtaining task-specific feature maps. Moreover, we propose an\nelement-wise addition of residual bias in the transformed feature space, which\nfurther helps stabilize GAN training in such settings. Our approach also\nleverages task similarity information based on the Fisher information matrix.\nLeveraging this knowledge from previous tasks significantly improves the model\nperformance. In addition, the similarity measure also helps reduce the\nparameter growth in continual adaptation and helps to learn a compact model. In\ncontrast to the recent approaches for continually-learned GANs, the proposed\napproach provides a memory-efficient way to perform effective continual data\ngeneration. Through extensive experiments on challenging and diverse datasets,\nwe show that the feature-map-transformation approach outperforms\nstate-of-the-art methods for continually-learned GANs, with substantially fewer\nparameters. The proposed method generates high-quality samples that can also\nimprove the generative-replay-based continual learning for discriminative\ntasks.\n