some leaves? or just a few? Or all of the leaves?

For some leaves (meaning it only affected that particular vine - follow it back to the tuber itself. If it was damaged, rotted out, then it affects only that part of the plant. Remove it.

One thing that causes sudden die offs is fungus. So check for this. If there is an overall die back - check the entire tuber for sponginess. It may have rotted out.

Usually with with sweet potatoes (and many other plants that are started off in water) you need to remove them from the water and slowly get it used to soiless mixes. They shouldn't have any prolonged stay in the water. (unless you use a hydrophonic system with specialized nutrients fed to the roots) The roots they develop in water do not easily adjust to soil which is why they need to be transplanted shortly after they develop those roots.

As a matter of practise, I prefer to start any plants in March or late Feb. because in my area (ontario) it's a long way off til May to transplant out. Earlier and things get too leggy or weak. Also all indoor plants do require good light.

Same problem with my sweet potato leaves when they turned brown and then died. Many have suggested over-watering as a cause; but I am not sure. Often the lower leaves become discolored first or one side of the plant. In some cases, the entire plant appears droopy and wilted.

fungus is what it is. sweet potato is meant to be cultivated in ground and prolonged cultivation in water leads to diseases such as fungus and bacteria. you can start them in water but as soon as young roots appear, plant them in soilless mixes until its time to set them outdoors.