I have read scriptures and looked at what it says of the heart of the fallen man, and what God had done with it concerning His creating a person anew.In my understanding, the soul is the carnal nature, or, in some translations, the flesh. This is a poor translation as the physical body is not capable of lusts, just physical sensations through which lusts are fulfilled. Much confusion has been caused by this and at this point, you would need to look into things to see if what I am saying is valid or not; otherwise, we'll just debate and spin our wheels forever. And who know, maybe create yet another denomination.
Regarding the corrupted flesh, Paul made it clear, as referring to the body where we are in, of which is of the dust of the earth, of which the body of Adam was made out of. It does not refer to the soul, or to the spirit.
Physical sensations are what is called “lust of the flesh” in contrast to the desires of the spirit, which are spiritual sensations, so to speak.
Tong
R4174