I don't know where they came from, except that it is likely they arrived in the region South and East of the Black Sea during the migrations of the peoples commonly known as Indo-European.
Peoples speaking what is sometimes called the Iranian language group are spread throughout the Central Asian regions ajoining.
Therefore I presume that the Persian peoples at least passed through Western Central Asia.
Please let me know if my logic is faulty or my information (such as it is) is mistaken.
My personal feeling, based on no evidence other than numerous tiny hints of ancient history, is that the origions of the language group commonly called Indo-European lies in a wide area from central asia into the Ukraine. Even some of the Germanic tribes entered known Roman history from off of the western plains.
So, you think their movement was from Asia toward Europe?