Here are some short speculative notes on the transmission of sin I’ve had written out for a while. I am mainly influenced here by Thomas’s comments in the Summa and this article https://www.jstor.org/stable/41974584 on Scotus.
Not semen per se but human matter (DNA) as the principle which transmits
If a sinful woman were to spontaneously generate, offspring sinful (reason is per above due to corrupted human matter being the material cause in generation. This is always why were a man now miraculously created from dirt, he would be sinless)
Though woman active, because father more active it seems we can say the father always wins out in deciding offspring condition (with regard to original sin, righteousness) [but also see Gerhard: “If the opposite were true, surely sin would have been propagated into their children. For though the mother may not be the active principle of generation, nevertheless she supplies the material which, on the basis of the hypothesis, was stained and contaminated by sin and which Eve would have communicated to the fetus. Thus from an unclean seed an unclean fetus would have been conceived and born.”]
Per above, precisely because God was more active than Mary, Christ born sinless
One interesting conclusion I thought I’d draw out: if there were two human races, one corrupt, the other not, the corrupt one could corrupt the pure one through their males breeding with their females (though this would be a pretty widespread assumption given it only applies to anyone who agrees males win out like Thomas does)