There was over 1,000 research participants of both sex, all age 60. They were measured for the presence of diabetes or pre-diabetes then followed for 15 years. Those who were diabetic were twice as likely to develop Alzheimer's and more likely (1.75x) to develop dementia of any type (Alzheimer's is a specific type which irreversibly forms plaques in brain tissue).
So what's the proposed link? Well, in diabetes, glucose remains in the bloodstream for a long time, waiting to be taken into cells but in the meantime floating around the bloodstream. Glucose which remains too long in the bloodstream leads to oxidative damage, hardening of the blood vessels (atherosclerosis) and glycosylation (think candied fruit but with blood vessels instead). All of this directly and indirectly compromises the body's ability to break down proteins, such as the amyloid protein which form the plaques found in Alzheimer's.
Two positive things have come of this research. One is that those with pre-diabetes did not show as significant a correlation with the development of Alzheimer's, so encourage your friends and family members in this situation to not wait for until pre-diabetes becomes diabetes. The second is that the research authors have already begun follow-up research looking at what Alzheimer's rates they find in diabetics who then control their blood sugar levels and risk factors. I'll keep you posted on the developments.