In which way proportional valves are controlled solely by current?
"Controlled by current" does not mean that no voltage is required (although that might be true in some specialized situations), it means that current is what determines the action of the valve. So you should adjust the voltage in order to maintain a certain current if you want the valve "position" to be relatively stable. That adjustment is done automatically by a "constant current" circuit. 

In the case of an electromagnet as in such a valve (or a relay for that matter) the mechanical force is proportional to the current through the coil**. The voltage, for a given current, will change depending on the temperature of the coil, so a constant current circuit should not only start off with a voltage dependent on the coil temperature, but it should increase the voltage across the coil as the coil self-heats.

** There will also be some change with the temperature of the materials involved in the magnetic circuit, but usually that's relatively small.