When a valid marriage has been contracted by two unbaptized persons, if one of them is afterwards baptized in the Catholic faith, and if the unbaptized party is unwilling to dwell peaceably with the Christian, the marriage can be entirely dissolved by this privilege, based on the teaching of Saint Paul (1 Corinthians 7:12-15)
"If any brother hath a wife that believeth not, and she consent to dwell with him, let him not put her away.
And if any woman hath a husband that believeth not, let her not put away her husband.
But if the unbeliever depart, let him depart.
For a brother or sister is not under servitude in such cases."
The Congregation of the Holy Office, at Rome, has jurisdiction in deciding cases under this privilege.
New Catholic Dictionary