Díaz was graduated as a medical surgeon in 1859, at the Universidad de Chile School of Medicine, when it was located on the building in the intersection of San Francisco and Las Delicias, the current Libertador General Bernardo O’Higgins Avenue. Two years later, he graduated as a Bachelor in Physical Sciences and Mathematics at the same university. He studied many diverse disciplines such as medicine, archeology, geology, seismology, climatology, ethnography and philosophy, and specialized in health geography, considered a prerequisite to specialization in parasitology and tropical diseases. His specialization allowed him to lead the sanitary commission to help the victims of the 1861 Mendoza earthquake.