I agree with the other answerer in that some self-examination will probably yield many ways in which you have overcome adversity or worked to support others from diverse backgrounds.
But here's another angle that's worth considering: Why does the university require a diversity statement in the first place? You'll encounter many forms of diversity at a large, public university like UCSB, where there is a substantial population of international students, federal student aid recipients, students with family/work obligations, and so on, and the school wants to know how you expect to integrate into the diverse community at the target university and how you believe interacting with a diverse student population will help you grow in your career and as a person.
Therefore, you don't have to "be" diverse (how can any individual be diverse?) to help foster a diverse, inclusive campus climate. I found this diversity statement from a faculty application written by an Asian American to be very successful, even though the author makes no mention of his personal background, focusing instead on the things he has done to support diverse students and explaining why he thinks diversity is a good thing:
I believe that diversity is fundamentally the relationship between a community’s distribution along a multitude of dimensions (e.g., physical traits, interests, cultures) and that of of the general population. I am strongly in favor of a diverse community that samples broadly from the general population. From a selfish perspective, it lets me learn from a variety of different, strange, and interesting people. From a larger perspective, it creates a robust community that is immune to "jumping on the band-wagon", and, as the UC diversity statement notes, it is "the source of innovative ideas and creative accomplishments".
In a case like yours, I would recommend being honest about your blind spots and expressing your interest in learning more about people from other backgrounds. What was it like to grow up and attend college within a homogeneous community? What challenges do you expect to face as you transition to the target university, and how will you overcome them? What are the characteristics of the university's community that attract you to studying there? Bonus points if you can name specific student organizations, courses, or other features of the university that align with these goals.
On the flip side, it's worth pointing out that writing a diversity statement isn't necessarily any easier for those who are from "diverse" backgrounds. A diversity statement that simply enumerates one's demographic characteristics without reflecting on the meaning and importance of diversity can ring hollow. And there is a danger in invoking false parallels, i.e. assuming "Because I am from marginalized community X, I understand the challenges faced by those from marginalized community Y."