Both Carbon and Iron have a strong affinity for Oxygen at high temperatures. Carbon's affinity for Oxygen is slightly greater than Iron's, which is why we can reduce Iron Oxide ores to Iron with Carbon; the basis of the iron making process throughout history.
Where there is only a little little Oxygen to be had, the Carbon tends to react with it, producing Carbon Dioxide gas which leaves the surface of the steel with a reduced Carbon content. At the high temperatures involved, Carbon diffusion occurs and Carbon tends to move from areas of high Carbon concentration to areas of low Carbon concentration. The diffusion is very temperature dependent and at typical HT temperatures, the Carbon gradient is quite steep; decarb tends to be near the surface.
At welding temperatures diffusion is much faster and the Carbon gradient much shallower. Decarb can be significant throughout the bar. Taking 1095 down to 1080-something is entirely possible and I am sure it happens to many beginners; working hot, working slowly and using a poorly-adjusted forge.
In general, it is probably fair to say that decarburization is permanent; there are methods of packing iron in a material with very high Carbon concentration, heating it and getting the Carbon to diffuse into the iron to make steel, but these are really part of the steelmaking process and tend to occur long before your average knifemaker starts getting involved. Look up the "cementation" process if you are interested.