The origins of AD are still pretty fuzzy. As far as it being T3DM, there's some evidence in that direction, but it's a bit mixed up with APOE.

It goes like this:

Neurons and a kind of glial cell called astrocytes are linked metabolically. The astrocytes have GLUT4 receptors like skeletal muscle cells; the astrocytes pass metabolites the neurons can more easily use (e.g. lactate) to them. If there's a block in the cascade that starts with insulin and ends up with little GLUT4 "glucose straws" poking up through the cell membrane, it's probably in the astrocytes — same receptors as striated muscle and adipocytes).

Meanwhile, if the neurons are very active, they produce lipids - plus reactive oxygen species. Combine the two and you get oxidated lipids which is super bad for cells, so instead the neurons export the lipids as APOE to the astrocytes, which turn them into droplets, and have no problem using them - which the neurons do (has to do with the way mitochondria are clumped - or not). Notice the type of lipid being exported...

Apologies for the hand-waving, wanted this to be short enough to fit in a response. If you're curious about the APOE transport between the two, maybe start here.