Separating Digital GND from Analog GND
There has to be a current path from GND on the converter to GND on the controller.  However, the AGND and DGND pins on the converter must be connected to each other (see http://www.analog.com/en/content/raq_groundingadcs/fca.html).  If noise may be an issue, then you could put a ferrite bead or LC filter in.  Definitely do not use a diode.