Just to add another Pope and Doctor to those already mentioned:
**Pope Innocent III, From the letter “Debitum pastoralis officii” **
You have, to be sure, intimated that a certain Jew, when at the point of death, since he lived only among Jews, immersed himself in water while saying: “I baptize myself in the name of the Father, and of the Son, and of the Holy Spirit, Amen.”
We respond that, since there should be a distinction between the one baptizing and the one baptized, as is clearly gathered from the words of the Lord, when he says to the Apostles: “Go baptize all nations in the name etc.” [cf. Matt. 28:19], the Jew mentioned must be baptized again by another, that it may be shown that he who is baptized is one person, and he who baptizes another. . . . If, however, such a one had died immediately, he would have rushed to his heavenly home without delay because of the faith of the sacrament, although not because of the sacrament of faith.
St. Alphonsus Liguori, Moral Theology, Bk. 6, nn. 95-7
Baptism, therefore, coming from a Greek word that means ablution or immersion in water, is distinguished into Baptism of water, of desire, and of blood.
We shall speak below of Baptism of water, which was very probably instituted before the Passion of Christ the Lord, when Christ was baptised by John. But baptism of desire is perfect conversion to God by contrition or love of God above all things accompanied by an explicit or implicit desire for true Baptism of water, the place of which it takes as to the remission of guilt, but not as to the impression of the [baptismal] character or as to the removal of all debt of punishment. It is called “of wind” because it takes place by the impulse of the Holy Ghost who is called a wind. Now it is de fide that men are also saved by Baptism of desire, by virtue of the Canon Apostolicam, “de presbytero non baptizato” and of the Council of Trent, session 6, Chapter 4 where it is said that no one can be saved “without the laver of regeneration or the desire for it.”