The artist was, from 1646, a pupil of Jacob Adriaensz. Backer in Amsterdam. After Backer's death in 1651, de Baen remained in that city until 1660, when he moved to The Hague, establishing himself as a popular painter of aristocratic portraiture, his clientele drawn to his style of flattering elegance, influenced by Van Dyck. According to Houbraken, he was called to England by King Charles II and worked for the court there; although there is no clear evidence, the painter was probably active in London at some time during the years 1661-65. De Baen also worked for the family of the Stadtholder (his portrait of the future Stadtholder and King William III is in the National Portrait Gallery, London) and for Frederick William, Elector of Brandenburg, who appointed him court painter in 1676 and tried unsuccessfully to lure him to Berlin.