On Dark Knowledge for Distilling Generators

Knowledge distillation has been applied on generative models, such as Variational Autoencoder (VAE) and Generative Adversarial Networks (GANs). To distill the knowledge, the synthetic outputs of a teacher generator are used to train a student model. While the dark knowledge, i.e., the probabilistic output, is well explored in distilling classifiers, little is known about the existence of an equivalent dark knowledge for generative models and its extractability. In this paper, we derive the first kind of empirical risk bound for distilling generative models from a Bayesian perspective. Through our analysis, we show the existence of the dark knowledge for generative models, i.e., Bayes probability distribution of a synthetic output from a given input, which achieves lower empirical risk bound than merely using the synthetic output of the generators. Furthermore, we propose a Dark Knowledge based Distillation, DKtill, which trains the student generator based on the (approximate) dark knowledge. Our extensive evaluation on distilling VAE, conditional GANs, and translation GANs on Facades and CelebA datasets show that the FID of student generators trained by DKtill combining dark knowledge are lower than student generators trained only by the synthetic outputs by up to 42.66%, and 78.99%, respectively.