Tradition
Socrates Scholasticus
Ecclesiastical History
Book 4 › Chapter 10
Birth of Valentinian the Younger
Soon after the conclusion of this war, and under the same consulate, a son was born to Valentinian, the emperor in the Western parts, to whom the same name as his father's was given. For Gratian had been born previously to his becoming emperor.
Source: Ecclesiastical History (New Advent)