In mainstream international relations theories, it is conventional to separate norm diffusion from norm evolution, and the consequence is the long-time neglect of norm evolution in the process of norm diffusion. This article introduces the concept of issue identity and highlights the agency of actors in order to provide a systematic explanation of the above question. Norm evolution in the process of norm diffusion hinges upon two conditions: differences of actors’ cognitive preferences and sensitivities to new norms. Issue identity determines actors’ cognitive preferences and definition of interests; differences of cognitive preferences lead to divergent understandings of norms. And the high degree of sensitivity to the change of norms and the subsequent adjustment of interests definition would transform cognitive differences to cognitive competition. Norm evolution in the process of norm diffusion takes place as actors engage in two-way persuasion and constantly adjust their cognitive structure. The result of norm diffusion-evolution is determined by where compromise is reached in terms of cognitive structure. After 1945, when maritime powers attempted to push for the global diffusion of the norm of freedom of navigation, they were confronted by the norm of sovereignty upheld by the developing countries. After the two sides conducted long-drawn two-way persuasion and reached a compromise, norm diffusion materialized, but the norm itself had changed from a strong one aiming at maximum freedom to a weak one with only limited freedom.