  Knowledge distillation aims to learn a lightweight student network from a
pre-trained teacher network. In practice, existing knowledge distillation
methods are usually infeasible when the original training data is unavailable
due to some privacy issues and data management considerations. Therefore,
data-free knowledge distillation approaches proposed to collect training
instances from the Internet. However, most of them have ignored the common
distribution shift between the instances from original training data and webly
collected data, affecting the reliability of the trained student network. To
solve this problem, we propose a novel method dubbed ``Knowledge Distillation
between Different Distributions" (KD$^{3}$), which consists of three
components. Specifically, we first dynamically select useful training instances
from the webly collected data according to the combined predictions of teacher
network and student network. Subsequently, we align both the weighted features
and classifier parameters of the two networks for knowledge memorization.
Meanwhile, we also build a new contrastive learning block called
MixDistribution to generate perturbed data with a new distribution for instance
alignment, so that the student network can further learn a
distribution-invariant representation. Intensive experiments on various
benchmark datasets demonstrate that our proposed KD$^{3}$ can outperform the
state-of-the-art data-free knowledge distillation approaches.
