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I'm sending additional materials (a LOCI and rec letter) to NYU, and was thinking of sending a diversity statement, however its not diversity as in URM, but diversity of experience. From what others have said, I seem to get the idea that NYU doesn't appreciate things like this, but wanted to ask specifically. Any thoughts?

Can't hurt to write one. I wrote a DS about an life experience and they still accepted me. If it's not too long, though, you could just put it in the LOCI.