I've had this problem with digital pedals before, they usually feed noise to other pedals via the daisy chain. I've tested plugging a digital pedal into the daisy chain and found it to introduce noise even when it's not plugged into the signal path.
A separate power supply will sort it, as will a fancy supply with multiple isolated outputs, or alternatively a Diago isolation adapter / Gigrig Virtual Battery should do the trick too (but check the max mA rating on those first).