From Samuel Angus’ The Mystery Religions:

Baptisms, or lustral purifications according to carefully prescribed forms, were required. Says Tertullian: ‘In certain Mysteries, e.g. of Isis and Mithra, it is by baptism (per lavacrum) that members are initiated… in the Apollinarian and Eleusinian rites they are baptized, and they imagine that the result of this baptism is regeneration and the remission of the penalties of their sins.’ Similarly Clement of Alexandria: ‘It is not without reason that in the Mysteries current among the Greeks lustrations hold the premier place.’ At Eleusis the mystae cleansed themselves in the sea. Apuleius, after prayer for pardon, underwent a bath of purification, and, after the vision of the deity, a baptism of sprinkling. After ten days’ castimonia the Dionysiac candidate was thoroughly cleansed before initiation. Ritual ablutions were originally assigned apotropaic efficacy; but, as the centre of gravity shifted from magic to religion, the symbolic and sacramental aspect of ablutions became more obvious than the apotropaic; but this did not arrest development in theories of baptism.

The union of ‘ water ‘ and ‘ spirit ‘ was a conception current in ancient religion which did not dissever the sign and the inner experience. The evidence for such baptisms and the importance attached thereto by antiquity, especially in religions of the Mystery type, has been greatly increased by recent discoveries. In the Hall of Initiation of the temple of Men at Pisidian Antioch there was found an oblong depression, of which the most obvious explanation is that it was lacus for baptism, not by bathing or immersion, as at Eleusis, but slighter. In the underground pagan shrine, discovered a few months ago on the Via Salaria, the most striking feature is a tank sunk deep in the floor which may well have served as a baptistery’ in some Mystery-religion.

Baptism was also viewed as a means or sacrament of regeneration, as clearly expressed by Tertullian above. Firmicus Maternus knew this conception in the Mysteries, but ‘there is another water, whereby men are renewed and reborn.’ Conspicuous among such baptisms was the Taurobolium, which was to the renatus his ‘spiritual birthday.’ In Titus III baptism is already the ‘ bath of regeneration’ accompanying renewal by the Spirit. In Hermas (Sim. IX. 16, 4) ‘the seal of the Son of God’ is water, ‘into which they descend dead and come up alive.’ In Gnosticism baptism was more important than even in orthodox Christianity. For the highest Mysteries a threefold baptism was required, of Water, Fire, and Spirit.