Díaz was born to a poor family in the small city of Santiago del Estero.
[1] In spite of a highly successful career, he remained loyal to his youth's companions, such as the Abalos brothers and percussionist Domingo Cura with whom Díaz recorded on many occasions.
In 1953 during a European tour, Hugo Díaz met with two admired musicians in Belgium: Larry Adler and Toots Thielemans.
[citation needed] He also played in the United States with Louis Armstrong and Oscar Peterson, and in La Scala, Milan with Renata Tebaldi and Mario del Monaco.
The sound of his harmonica was captured in the song Milonga Triste included in the film The Tango Lesson, directed by Sally Potter.