  This paper investigates the accuracy of generative models and the impact of
knowledge transfer on their generation precision. Specifically, we examine a
generative model for a target task, fine-tuned using a pre-trained model from a
source task. Building on the "Shared Embedding" concept, which bridges the
source and target tasks, we introduce a novel framework for transfer learning
under distribution metrics such as the Kullback-Leibler divergence. This
framework underscores the importance of leveraging inherent similarities
between diverse tasks despite their distinct data distributions. Our theory
suggests that the shared structures can augment the generation accuracy for a
target task, reliant on the capability of a source model to identify shared
structures and effective knowledge transfer from source to target learning. To
demonstrate the practical utility of this framework, we explore the theoretical
implications for two specific generative models: diffusion and normalizing
flows. The results show enhanced performance in both models over their
non-transfer counterparts, indicating advancements for diffusion models and
providing fresh insights into normalizing flows in transfer and non-transfer
settings. These results highlight the significant contribution of knowledge
transfer in boosting the generation capabilities of these models.
