In the Orthodox tradition especially, the answer has been that in the Incarnation God united with sinful human flesh. Thus, what Jesus carried down into the baptismal waters was the sin-bearing flesh of all of humanity, which was then cleansed in the Jordan.
In short, Jesus baptized us--all of humanity--in the Jordan.
This idea is beautifully captured in an ancient baptismal homily by Narsai, from the fifth century. Jesus speaking of his baptism:
Let it be so! I am being baptized as one deficient and in need of mercy,
so that I may fill up in my person what is lacking in the human race.
From the same race that has succumbed to sin I am also.
Let it be so! I am paying for the bond that Adam wrote in Eden.
From the same clay that passions have overwhelmed is my structure.
Let it be so! I am heating our weak clay in the water of the Spirit.
I am from the same lineage that death has swallowed and defrauded of its life.
Let it be so! I am descending in mystery into the water and raising it up.
I am a member of the race that is captive to the evil one of its own accord.
I will go forth to bring back our captive race from the rebel.
A bond of death my forefathers wrote out and succumbed to sin;
and I have made an agreement that I will pay for it in mystery first of all...
If I do not scour away bodily filth in my own person, the body will not be purified;
And if it does not descend with me to baptism, it will not receive pardon.
