A review and a large study have recently added to the growing evidence that type 2 diabetes is not only a risk factor for Alzheimer's, but is also linked to poorer cognitive function and faster age-related cognitive decline. The amount of this also seems to be related to glucose control in a dose-dependent manner.
Somewhat surprisingly, there is evidence that the association is not linked to vascular factors, but is in significant part explained by neuron loss. That part is not surprising — brains 'naturally' shrink with age, and growing evidence points to the importance of exercise (which promotes the growth of new neurons) in combating that loss. If diabetics are less likely to exercise (which seems likely, given the strong association with obesity), this may, at least in part, account for the greater brain atrophy.
Type 2 diabetes linked to poorer executive function
A meta-analysis of 60 studies involving a total of 9815 people with Type 2 diabetes and 69,254 control individuals, has found a small but reliable association between diabetes and poorer executive function. This was true across all aspects of executive function tested: verbal fluency, mental flexibility, inhibition, working memory, and attention.
Unfortunately, effective diabetes management does depend quite heavily on executive function, making this something of a negative feedback cycle.
Diabetes in midlife linked to greater age-related cognitive decline
A long-running U.S. study involving 13,351 adults, has found that cognitive decline over 19 years was 19% greater among those who had diabetes in midlife. Moreover, cognitive decline increased with higher hemoglobin A1c level and longer duration of diabetes.
At the beginning of the study, participants were aged 48-67 (median: 57), and 13% of participants were diagnosed as diabetic. Cognition was tested using delayed word recall, digit symbol substitution, and word fluency tests.
The findings support the view that glucose control in midlife is important to protect against cognitive decline later in life.
Brain atrophy linked with cognitive decline in diabetes
A 2013 study showed that almost half of the cognitive impairment seen among diabetics was explained by their loss of gray matter.
Brain scans and cognitive tests of 350 people with Type 2 diabetes and 363 people without diabetes revealed that those with diabetes had more cerebral infarcts and greater shrinkage in specific regions of the brain. Diabetes was associated with poorer visuospatial memory, planning, visual memory, and processing speed. These associations were independent of vascular risk factors, cerebrovascular lesions, or white matter volume, but almost half of the associations were explained by the shrinkage of gray matter in the hippocampus and across the brain.
Vincent, C. & Hall, P.A. 2015. Executive Function in Adults With Type 2 Diabetes: A Meta-Analytic Review. Psychosomatic Medicine, doi: 10.1097/PSY.0000000000000103
 Diabetes in midlife and cognitive change over 20 years: a cohort study. Annals of Internal Medicine. 2014 ;161(11):785 - 793.
 Brain Atrophy in Type 2 Diabetes Regional distribution and influence on cognition. Diabetes Care [Internet]. 2013 ;36(12):4036 - 4042. Available from: http://care.diabetesjournals.org/content/36/12/4036