Linear voltage regulator current source high side/low side regulation
The DC current at the through D1 will be the same as the DC current through D2. C2 is suggested by the manufacturer, and probably necessary for stability.
C1 may not be required. You might want to check that there is not a current spike through the input when 300V is suddenly applied (after a long time with no power and after short times). Also consider a resistor on the input (may affect stability). Neither capacitor has much voltage across it with single LEDs and under normal conditions.
Since you have 60V to play  with you might also want to consider a series diode on the input eg. M7/1N4007.