His first formal training was with the Cremonese painter Cesare Baglioni (no evident relation to Giovanni Baglione).
He apparently quickly worked independently then rejoined his friend and fellow Bolognese and Baglione pupil, Lionello Spada.
They soon parted, with Spada becoming a canvas painter, and Curti was to travel to paint in Modena, Parma (1618 and 1630), Rome (1623) and Genoa.
He returned from Rome to Bologna, and there was assisted by Michelangelo Colonna, Agostino Mitelli, and Andrea Seghizzi, and painted architectural backgrounds for Guercino frescoes.
The main source of his biography is Cesare Malvasia, whose father's villa at Trebbio was frescoed by Curti and assistants.