"cultural diversity" is a noun "culturally diverse" is an adjective

I agree with the comments that say one is a noun and the other is an adjective, but then it's also necessary to define what the noun means. I think there's a certain amount of flexibility about this (because it's still a relatively new term) , but 'cultural diversity ' is often used to express a concept, or belief. Whereas the adjective is more a statement of fact (though it might be difficult to measure). For example, if a school says that it believes in cultural diversity, then you would expect to find evidence of activities such as studying religious festivals from various religions or the history of different countries. But if you just said that the school is culturally diverse, you might just mean it has students from many different backgrounds, but the curriculum could still be mono cultural

for example: Cultural diversity is important. In big cities, society is often culturally diverse.

I agree with Franz.