Can you be more precise because distortion could be any type of sound deemed offensive and in some cases even liked. Is it a hiss, smear, crack, brightness, shoutiness?
Electrically the Kaede is a much easier load than the Heaven in every way imaginable. It's frequency response is a mess but that's a problem for your ears not the amp
People were getting weird sounds which they call noise, but not the noise we are accustomed to hearing like hiss. There was a Korean user that was using an impedance adapter with his LCD-X to take out this sound or noise. LCD-X is resistive and low impedance. Some dynamic drivers are low impedance and close to flat impedance graph. I have heard this issue for my Galaxy S4 for low impedance phones, but it happened with BA iems also. What it did was distorted the bass creating distortion. IT was fixed by firmware upgrade.
I finally have time to answer this. SilverEars description sounds about right although I have not tried full size cans like the LCD-X. With the Kaede, the issue was especially obvious on one song where a bass line produced a distorted echo in my right earpiece. This did not happen with the Heaven VI or ES5 both of which drive super clean. If I then turned the M to line out mode, i.e. maximum volume at high gain producing an output of 1.2 Vrms, and then placed the Quickstep amp between it and the Kaede, the distortion disappeared and the Kaede (within its funky harmonic resonance sound profile) sounds fantastic. Actually it sounds as good as it ever has. So with the M outputting at maximum volume, and feeding an amp renowned for its black background, producing excellent results, the issue should not be background noise of the M. There is something in the circuit created by the M directly driving the Kaede that is causing distortion. I believe that it is the zero ohm impedance, in no small part because the problem is quite unique in the DAP world and there is no other satisfactory explanation.
My FAD 1601SC and 1602SS have similar issues with a smeared distorted sound directly from the M that completely disappears with the introduction of an intermediary amp. Again, my BA IEMs sound fantastic and
uber clean directly driven by the M.
All the mathematical / damping factor logic in the world will not make this issue go away. At a certain point we have to avoid being like the economist who says 'there cannot be a ten dollar bill by my foot because if there was, someone else would already have picked it up.' It is there!
I have these 1 ohm resistors on the way.
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=190822877396&ssPageName=ADME:L:OC:CA:3160
Hopefully once I use my multimeter to isolate a matched pair, they will be of sufficient quality to create a good adapter cable, test the above theory, and hopefully make the issue go away altogether. (In the short run, I will have the 15 ohm adapter Monday for testing.)
Time will tell how all of this plays out.