Type 1 diabetes is caused by insufficient insulin production.
Unlike in muscle and adipose tissue (GLUT4), glucose uptake by the liver is by GLUT2 and thus insulin-independent. Consequently, under very high blood glucose concentrations, glucose will move by facilitated diffusion into the liver.
However, insulin is not available to stimulate glycogenesis, or lipogenesis; glucagon will be secreted due to high blood glucose concentration, doing the opposite. What happens to this glucose? Does it simply diffuse back out (GLUT2 is bidirectional)? Presumably glucokinase produces glucose-6-phosphate, but the highly controlled points of glycolysis (e.g. PFK-1) will lack stimulation due to loss of insulin. Does a lack of glucagon (due to glucose still reaching pancreatic islet cells, also via GLUT2) have a positive effect?