Objection 1. It would seem that the sin of the first parent is not transmitted, by the way of origin, to all men. Because death is a punishment consequent upon original sin. But not all those, who are born of the seed of Adam, will die: since those who will be still living at the coming of our Lord, will never die, as, seemingly, may be gathered from 1 Thessalonians 4:14: "We who are alive... unto the coming of the Lord, shall not prevent them who have slept." Therefore they do not contract original sin.
Objection 2. Further, no one gives another what he has not himself. Now a man who has been baptized has not original sin. Therefore he does not transmit it to his children.
Objection 3. Further, the gift of Christ is greater than the sin of Adam, as the Apostle declares (Romans 5:15, seqq). But the gift of Christ is not transmitted to all men: neither, therefore, is the sin of Adam.
On the contrary, The Apostle says (Romans 5:12): "Death passed upon all men in whom all have sinned."
I answer that, According to the Catholic Faith we must firmly believe that, Christ alone excepted, all men descended from Adam contract original sin from him; else all would not need redemption [Cf. Translator's note inserted before TP, 27] which is through Christ; and this is erroneous. The reason for this may be gathered from what has been stated (1), viz. that original sin, in virtue of the sin of our first parent, is transmitted to his posterity, just as, from the soul's will, actual sin is transmitted to the members of the body, through their being moved by the will. Now it is evident that actual sin can be transmitted to all such members as have an inborn aptitude to be moved by the will. Therefore original sin is transmitted to all those who are moved by Adam by the movement of generation.
Reply to Objection 1. It is held with greater probability and more commonly that all those that are alive at the coming of our Lord, will die, and rise again shortly, as we shall state more fully in the TP (XP, 78, 1, Objection 1). If, however, it be true, as others hold, that they will never die, (an opinion which Jerome mentions among others in a letter to Minerius, on the Resurrection of the Body--Ep. cxix), then we must say in reply to the objection, that although they are not to die, the debt of death is none the less in them, and that the punishment of death will be remitted by God, since He can also forgive the punishment due for actual sins.
Reply to Objection 1. Original sin is taken away by Baptism as to the guilt, in so far as the soul recovers grace as regards the mind. Nevertheless original sin remains in its effect as regards the "fomes," which is the disorder of the lower parts of the soul and of the body itself, in respect of which, and not of the mind, man exercises his power of generation. Consequently those who are baptized transmit original sin: since they do not beget as being renewed in Baptism, but as still retaining something of the oldness of the first sin.
Reply to Objection 3. Just as Adam's sin is transmitted to all who are born of Adam corporally, so is the grace of Christ transmitted to all that are begotten of Him spiritually, by faith and Baptism: and this, not only unto the removal of sin of their first parent, but also unto the removal of actual sins, and the obtaining of glory.
Source: Summa Theologica (New Advent)