Well, not really, or not of the kind you seem to imagine, because the presuppositions of your question are incorrect. Constantine didn't convert the whole empire to Christianity in 313, that statement is wrong on several levels.

Firstly, after the Battle of Milvian Bridge, the degree of Constantine's own 'conversion' is debated. Nonetheless, the Edict of Milan in 313 is a major turning point, because Constantine secures agreement with Licinius, who is from 313 Augustus in the East, to proclaim religious toleration. This ends, from an imperial standpoint, legal persecution of Christians (and other religious groups, the Edict proclaims general religious toleration). It is aimed, in part, against Maximinus Daia in the East, who was all in favour of persecuting the Christians. Keep in mind, too, that Licinius was not a Christian.

So the Edict of Milan doesn't make anyone Christian, it stops it being legal to persecute them, and it acts to provide restitution for past wrongs (mainly restoration of goods and property taken from them). It is part of Constantine's decisive move towards Christianity, and it is part of Constantine's very first steps of officially favouring Christianity, which continues and develops throughout his reign.

It is not (a) making the State Religion Christianity, (b) converting the Empire. The former happens under Theodosius, the latter is best represented as a process that goes on throughout the 4th century.

I hope that clarifies why this question is founded upon false premises.