Sublime does mean to purify too, and the process of purification involves the sublimation of a compound (which is the transformation from solid to gas state, as you mentioned). Here is a quote from wikipedia:

“Sublimation is a technique used by chemists to purify compounds. Typically a solid is placed in a vessel which is then heated under vacuum. Under this reduced pressure the solid volatilizes and condenses as a purified compound on a cooled surface.”

My Chambers dictionary gives “to purify by sublimation”.

As for the psychology angle, “to direct unconsciously (a primitive impulse such as an aggressive or sexual impulse) into a higher or more socially acceptable action; to direct into a higher channel. (chem) a product of sublimation, especially a corrosive sublimate.

Sublimate means to transform directly from the solid to the gas state, as dry ice does. It does not mean to purify.