In this blog post, we delve into knowledge distillation techniques for Large Language Models (LLMs), with a particular focus on using Kullback-Leibler (KL) Divergence as the optimization objective. Knowledge distillation is a powerful tool to reduce model size while maintaining comparable performance, making it especially useful in scenarios with constrained computational or serving resources. We specifically explore the nuances of Forward KL divergence and Reverse KL divergence, examining their roles in the distillation process. By comparing these two approaches, we aim to uncover their behaviours, strengths, and practical applications in LLM distillation.