Díaz grew up in Atlanta and attended the New England Conservatory of Music as an undergraduate. He also holds a degree in industrial design. Díaz went on for further classes at the Curtis Institute. He has studied with his father, Manuel Díaz, Louis Krasner, and Joseph de Pasquale, among others, and held positions as principal viola of the National Symphony under Mstislav Rostropovich, a member of the Boston Symphony under Seiji Ozawa, and a member of the Minnesota Orchestra under Sir Neville Marriner. In 1996 Díaz succeeded de Pasquale as principal violist of the Philadelphia Orchestra, remaining in that position until 2006. Díaz has played concertos with leading orchestras in the Americas, Europe, and Asia. He has premiered works by Krzysztosf Penderecki, Jennifer Higdon, and Edison Denisov, and has performed chamber music in the Díaz Trio with his brother, cellist Andrés Díaz, and violinist Andrés Cárdenes. Díaz's recording career began in 2002 with a CD of virtuoso viola-and-piano music of Henri Vieuxtemps and included an album of viola arrangements by William Primrose, whose 1600 Amati instrument Díaz acquired.
As director of the Curtis Institute, Díaz has developed innovative initiatives. The Curtis on Tour program has taken Díaz on worldwide tours with Curtis students and other faculty. He has overseen building projects that have doubled the size of the school's Philadelphia campus, and he has instituted a new classical guitar department and new conducting and string quartet programs. The Curtis Summerfest has offered public summer courses, and the Curtis Performs program has begun an online programming presence. In the fall of 2013 Curtis began offering online courses via the Coursera website, becoming the first classical music conservatory to do so.
Díaz is married to violinist Elissa Lee Koljonen, with whom he has frequently performed. The pair met when both were performing at a music festival on Cape Cod. ~ James Manheim, Rovi