This paper addresses the challenge of knowledge distillation between large language models with different tokenizers. The authors systematically analyze the attention mechanism of Dual-Space Knowledge Distillation with Cross-Model Attention (DSKD-CMA), revealing its strengths and limitations through token alignment probing and visualization. They propose DSKD-CMA-GA, a novel method leveraging Generative Adversarial learning to better align mismatched key-query distributions across models. Experimental results demonstrate consistent improvements in text generation quality as measured by ROUGE-L scores, offering a more transparent and effective approach to compressing large language models for efficient deployment.