Deep generative models have received significant attention in recent years due to their impressive capabilities across a variety of applications and domains. However, one of the primary challenges these models face is their computational intensity, which complicates deployment on edge devices with limited resources. Knowledge distillation emerges as an effective solution for creating lightweight models. In this paper, we present a comprehensive review of the latest advancements in knowledge distillation as a strategy for creating lightweight models. This review aims to provide an analysis of knowledge distillation techniques in deep generative models, highlighting key principles, and discussing existing approaches.