Diggs was born in Oakland, California, the son of Barbara, a social worker, and Dountes Diggs, a bus driver. His mother is Jewish, and his father is African-American. His parents named him "Daveed", the Hebrew pronunciation of David. Diggs has said, "'David' means beloved in Hebrew... They spelled it with two E's because my dad liked the look of it.” His parents' ethnic/racial identities have contributed to his own self-identification: "The cultures never seemed separate—I had a lot of mixed friends. When I was young, I identified with being Jewish, but I embraced my dad's side too.
Diggs is an alumnus of Berkeley High School and Brown University, where he graduated in 2004 with a bachelor's degree in theatre arts. He was recruited by Brown for his track skills, and broke the Brown Bears' school record in the 110 meter hurdles as a sophomore with a time of 14.21 seconds. After graduating, he worked as a substitute teacher.
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