Knowledge distillation aims to transfer knowledge from a large teacher model to a compact student counterpart, often coming with a significant performance gap between them. Interestingly, we find that a too-large performance gap can hamper the training process.To alleviate this, we propose a Gap Preserving Distillation (GPD) method that trains an additional dynamic teacher model from scratch along with the student to maintain a reasonable performance gap. To further strengthen distillation, we develop a hard strategy by enforcing both models to share parameters. Besides, we also build the soft bidirectional mappings between them through Inverse Reparameterization (IR) and Channel-Branch Reparameterization (CBR).IR initializes a larger dynamic teacher with approximately the same accuracy as the student to avoid a too large gap in early stage of training. CBR enables direct extraction of an effective student model from the dynamic teacher without post-training. In experiments, GPD significantly outperforms existing distillation methods on top of both CNNs and transformers, achieving up to 1.58\% accuracy improvement. Interestingly, GPD also generalizes well to the scenarios without a pre-trained teacher, including training from scratch and fine-tuning, yielding a large improvement of 1.80\% and 0.89\% on ResNet18, respectively.