The following selection of quotations is for those who, like me, have at some time found themselves pondering the differences between infant and adult baptism. Obviously, under discussion and consideration here are not two different kinds of baptism— we confess one baptism for the remission of sins. Anyway, it’s interesting and (I think) enlightening to see how the seventeenth-century Lutheran orthodox dogmaticians, a.k.a. the Lutheran scholastic theologians, engaged the topic. You may find their ratiocinations convincing and/or helpful, you may not. Enjoy.
In opposition to the assertion of the Papal Church, that “sin is destroyed by Baptism, so that it no longer exists,” the doctrine of the forgiveness of sins by Baptism is thus more particularly defined: “The guilt and dominion of sin is taken away by Baptism, but not the root or incentive (fomes) of sin.” (Holl. [David Hollatz], 1096) Ap. Conf. [Apology of the Augsburg Confession] (I, 35): “(Luther) always thus wrote, that Baptism removes the guilt of original sin, although the material of sin, as they call it, may remain, i.e., concupiscence. He also affirmed of this material, that the Holy Spirit, given by Baptism, begins to mortify concupiscence and creates new emotions in man. Augustine speaks to the same effect when he says: ‘Sin is forgiven in Baptism, not that it does not exist, but that it is not imputed.’”
 Grh. [Johann Gerhard] (IX, 236): “There is no other ordinary means of regeneration than the Word and the Sacrament of Baptism. By the Word infants cannot be influenced, but only adults, who have come to years of discretion. It remains, therefore, that they are regenerated, cleansed from the contagion of original sin, and made partakers of eternal life, through Baptism.”
 Br. [Johann Wilhelm Baier] (690): “But here, as regards the immediate design [of Baptism] a diversity exists in respect to the different subjects. For faith is at first conferred upon and sealed to all infants alike by Baptism, and by this faith the merit of Christ is applied to them. But adults, who receive faith from hearing the Word before their Baptism, are only sealed and confirmed in their faith by it. (Examples, Acts 2:41; 8:12, 36–38; 16:14, 15, 31, 33; 18:8.) And not only now, when Baptism is received, but afterwards, and throughout their whole life, it efficaciously contributes to the confirmation of their faith and further renewal.”
Grh. (IX, 169): “To infants Baptism is, primarily, the ordinary means of regeneration and purification from sin; … secondarily, it is the seal of righteousness and the confirmation of faith; to adult believers it serves principally as a seal and testimony of the grace of God, sonship and eternal life, but in a less principal sense it increases renovation and the gifts of the Holy Spirit. Infants by Baptism receive the first fruits of the Spirit and of faith; adults, who through the Word have received the first fruits of faith and of the Holy Spirit, procure an increase of these gifts by Baptism.”
Hfrffr. [Matthias Hafenreffer] (500): “But what? Suppose one is regenerated by the Word. Has he need of Baptism also? And can Baptism be said to be to him the laver of regeneration? Answer: Both. For believers, too, ought to be baptized, unless they be excluded by a case of necessity. And when they are baptized, Baptism is truly to them the laver of regeneration, because it augments regeneration, wrought by the Word, by a wonderful addition; because, also, the sacramental act seals the regeneration of faith to absolute certainty.”
 Although Baptism, where it is rightly performed, is a Sacrament and offers saving grace, without any respect to the faith of the recipient, yet it is also true that, in the case of adults, a beneficial result follows only where Baptism is received by faith. The question: Is a hypocrite, therefore, also regenerated, if he receive Baptism? is thus answered by Hfrffr. (499): “In such a case we must distinguish between the substance of Baptism and its fruits. For a hypocrite, if he be baptized, receives indeed true Baptism, as to its substance, which consists in the legitimate administration of the Sacrament according to the words of the institution and in the promise of divine grace. But as long as he perseveres in his hypocrisy and infidelity, he is destitute of its salutary fruits and effects, which only believers experience. There fore, God really offers his grace and the forgiveness of sins to him who is baptized, and desires on his part to preserve that covenant perpetually firm and entire without any change, so that the grace promised in the covenant may always be accessible to him who is baptized, and that he may enjoy it as soon as he repents; but, as long as he remain a hypocrite and impenitent, he is destitute of it.” Quen. [Johannes Andreas Quenstedt] (IV, 117): “Even to all hypocrites Baptism offers spiritual gifts, as regeneration and whatever is comprehended under it, the gift of faith, remission of sins, etc., … but some adults, by actual impenitence, hypocrisy, and obstinacy, defraud themselves of the saving efficacy of Baptism; and hence, although these gifts be offered to them, they are not actually conferred; yet, in the meantime, it is and remains in itself a salutary organ and means of regeneration, since the deprival of the first act does not follow from the deprival of the second act through some fault of the subject.” Cat. Maj.[Large Catechism] (IV, 33): “Faith alone makes the person worthy to receive profitably this salutary and divine water. For, as this is offered and promised to us in the words together with the water, it cannot be received otherwise than by cordially believing it. Without faith, Baptism profits nothing; although it cannot be denied that in itself it is a heavenly and inestimable treasure.”
Source: Heinrich Schmid, The Doctrinal Theology of the Evangelical Lutheran Church, Verified from the Original Sources. C. A. Hay & H. E. Jacobs, Trans. Second English Edition, Revised according to the Sixth German Edition, Philadelphia, PA: Lutheran Publication Society, 1889; pp. 549–551
Free Reprint of Schmid in PDF— not a facisimile edition!— from CCEL here.