Popular deep-learning models in the field of image classification suffer from catastrophic forgetting---models will forget previously acquired skills when learning new ones. Generative replay (GR), which typically consists of a generator and a classifier, is an efficient way to mitigate catastrophic forgetting. However, conventional GR methods only focus on a single instruction relationship (generator-to-classifier), where the generator synthesizes samples for previous tasks to instruct the training of the classifier, while ignoring the ways in which the classifier can benefit the generator. In addition, most generative replay methods typically reuse the generated samples to update the generator, which causes the samples regenerated by the generator deviating from the distribution of previous tasks. To overcome these two issues, we propose a novel approach, called deep diffusion-based generative replay (DDGR), which adopts a diffusion model as the generator and calculates an instruction-operator through the classifier to instruct the generation of samples. Extensive experiments in class incremental (CI) and class incremental with repetition (CIR) settings demonstrate the advantages of DDGR. Our code is available at https://github.com/xiaocangshengGR/DDGR.