Its a constant current driver, no need to worry about the diode voltage (so long as your supply voltage is at least diode voltage (4.4v) + 2v or so for the driver.
In other words: Say you are feeding the driver with 12v; you can short out the output and it will happily supply the set current in to the short circuit. It will supply this set current up to a forward voltage of around 10v (so you could run 2 diodes in series to more or less at full power whilst only loading the driver with 1A, then remove one diode from the circuit and nothing will change, the driver will still only push 1A through the single diode).
Hope that's clear

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