Ambrose, teaching the newly baptized, explains the white robes they now wear:
After this white robes were given to you as a sign that you were putting off the covering of sins, and putting on the chaste veil of innocence, of which the prophet said: "Thou shalt sprinkle me with hyssop and I shall be cleansed, Thou shalt wash me and I shall be made whiter than snow."
For he who is baptized is seen to be purified both according to the Law and according to the Gospel: according to the Law, because Moses sprinkled the blood of the lamb with a bunch of hyssop; according to the Gospel, because Christ's garments were white as snow, when in the Gospel He showed forth the glory of His Resurrection. He, then, whose guilt is remitted is made whiter than snow. So that God said by Isaiah: "Though your sins be as scarlet, I will make them white as snow."
The angels, too, were in doubt when Christ arose; the powers of heaven were in doubt when they saw that flesh was ascending into heaven. Then they said: "Who is this King of glory?" And whilst some said "Lift up your gates, O princes, and be ye lift up, ye everlasting doors, and the King of glory shall come in." In Isaiah, too, we find that the powers of heaven doubted and said: "Who is this that cometh up from Edom, the redness of His garments is from Bosor, He who is glorious in white apparel?"
But Christ, beholding His Church, for whom He Himself, as you find in the book of the prophet Zechariah, had put on filthy garments, now clothed in white raiment, seeing, that is, a soul pure and washed in the layer of regeneration, says: "Behold, thou art fair, My love, behold thou art fair, thy eyes are like a dove's," in the likeness of which the Holy Spirit descended from heaven. The eyes are beautiful like those of a dove, because in the likeness of a dove the Holy Spirit descended from heaven.
On the Mysteries, 7, 34, 36-37