Regularization-based methods are beneficial to alleviate the catastrophic forgetting problem in class-incremental learning. With the absence of old task images, they often assume that old knowledge is well preserved if the classifier produces similar output on new images. In this paper, we find that their effectiveness largely depends on the nature of old classes: they work well on classes that are easily distinguishable between each other but may fail on more fine-grained ones, e.g., boy and girl. In spirit, such methods project new data onto the feature space spanned by the weight vectors in the fully connected layer, corresponding to old classes. The resulting projections would be similar on fine-grained old classes, and as a consequence the new classifier will gradually lose the discriminative ability on these classes. To address this issue, we propose a memory-free generative replay strategy to preserve the fine-grained old classes characteristics by generating representative old images directly from the old classifier and combined with new data for new classifier training. To solve the homogenization problem of the generated samples, we also propose a diversity loss that maximizes Kullback Leibler (KL) divergence between generated samples. Our method is best complemented by prior regularization-based methods proved to be effective for easily distinguishable old classes. We validate the above design and insights on CUB-200-2011, Caltech-101, CIFAR-100 and Tiny ImageNet and show that our strategy outperforms existing memory-free methods with a clear margin. Code is available at https://github.com/xmengxin/MFGR
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