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Deep long-tailed learning aims to train useful deep networks on practical, real-world imbalanced distributions, wherein most labels of the tail classes are associated with a few samples. There has been a large body of work to train discriminative models for visual recognition on long-tailed distribution. In contrast, we aim to train conditional Generative Adversarial Networks, a class of image generation models on long-tailed distributions. We find that similar to recognition, state-of-the-art methods for image generation also suffer from performance degradation on tail classes. The performance degradation is mainly due to class-specific mode collapse for tail classes, which we observe to be correlated with the spectral explosion of the conditioning parameter matrix. We propose a novel group Spectral Regularizer (gSR) that prevents the spectral explosion alleviating mode collapse, which results in diverse and plausible image generation even for tail classes. We find that gSR effectively combines with existing augmentation and regularization techniques, leading to state-of-the-art image generation performance on long-tailed data. Extensive experiments demonstrate the efficacy of our regularizer on long-tailed datasets with different degrees of imbalance.