There has been a study in mice showing that consumption of artificial sweeteners changes the composition of microbiota in their guts, and seems to change it in a way that makes the mice more susceptible to diabetes.
See the 2014 Nature article Artificial sweeteners induce glucose intolerance by altering the gut microbiota.
From the abstract:
Here we demonstrate that consumption of commonly used NAS [non-caloric artificial sweetener] formulations drives the development of glucose intolerance through induction of compositional and functional alterations to the intestinal microbiota.
This at least gives a possible pathway linking artificial sweeteners and diabetes, thus allowing for the possibility that the correlation discovered by the study cited by the Daily Mail arises because artificial sweeteners help cause diabetes in humans.
It might also explain why this effect doesn't depend on the composition of the artificial sweeteners. The effect in the mice was present for all three artificial sweeteners tested—saccharin, sucralose and aspartame.
One possible mechanism for this effect (my speculation) is that it could be caused by the stomach signaling the gut microbiota that calories are coming, and then not actually producing any calories. If this is the mechanism, then non-caloric natural sweeteners might also be correlated with diabetes.
As far as I know, there isn't any definitive evidence for this in humans yet.