Quantization noise on DUE DAC

I am trying to make use of the DACs on the DUE for a project, but they seem to have quite abit of what appears to be Quantization noise. After being written to, the DACs seem fluctuate randomly in discrete steps at the 1-3 bit level @ 10 kHz(see attached picture, both DACs LP filtered at 300 kHz). Is this to be expected? Does anyone know why this happens?

void setup() {  
    analogWriteResolution(12);
}

void loop() {
analogWrite(DAC1, 1000); 
analogWrite(DAC0, 1000);
while(true){};
}

edit: Seems like I am not the first...Horrific DAC noise on DUE board - Arduino Due - Arduino Forum

I have not read anything about this issue, but IMO for a serious leverage of the DACs, one should use DACC registers programming rather than the analogWrite() function. E.g. DACC_MR_REFRESH() 8 bits in DACC->DACC_MR should not be at 0, the minimum should be 1.