The words difference, divergence, and diversity are all nouns that indicate dissimilarity or variation, or a condition, state, or quality of not being alike, the same, or together. To understand how the words are different, and how they are used, look at the definitions and examples of each:
1 : the quality that makes one person or thing unlike another
Example: The difference between the houses is that one is red and the other is blue.
2 : something that people do not agree about
Example: The boys had too many differences and could not remain friends.
3 : the amount by which things differ
Example: There is a 2-year age difference between the sisters.
1 : an act or instance of moving or drawing apart
Example: The road and the river ran parallel with only a short divergence near the middle of the town.
2 : a departure from a course or direction
Example: The company's divergence from their usual marketing strategy shocked consumers.
1 : the quality or state of having many different forms, types, ideas, etc.
Example: They came up with a solution quickly because of the diversity of ideas presented in the meeting.
2 : the state of having people who are different races or who have different cultures in a group or organization
Example: The cultural and racial diversity among the students enriched the school's educational environment.
Even though they are similar, we can see that each word has a meaning a little different from the other two.
The core meaning of difference is that something is unlike something else in some way.
The core meaning of divergence is that two or more things, ideas, opinions, or actions are moving apart or becoming unalike.
The core meaning of diversity is that there are many dissimilar or unlike forms, types, or ideas present in one area, group, or organization.
I hope this helps.