These might be allowed on the vegan Ma-Pi 2 diet
A vegan diet was superior to a low-fat diet over the course of three weeks, in terms of blood sugar, hemoglobin A1c, total cholesterol and LDL cholesterol. The vegans were also able to use fewer drugs.
A specific vegan diet (Ma-Pi 2) was compared to a low-fat diet in a study published by Nutrition & Metabolism. Carbsane Evelyn dove into the study at her blog (recommended reading), or you can read the original research report yourself. Study subjects had fairly well-controlled type 2 diabetes and were elderly (66) and overweight (84 kg or 185 lb). The vegan diet was mostly whole grains, vegetables, legumes, and green tea. The low-fat and vegan diets both probably supplied 200–300 calories/day fewer than what the subjects were used to: 1900 cals for men, 1700 for women. The study had 25 patients in each group and lasted only three weeks.
The vegan group ate 335 grams/day of carbohydrate compared to 235 grams in the low-fat group. In contrast, the Low-Carb Mediterranean Diet provides 30–100 grams/day of digestible carb and the Ketogenic Mediterranean Diet allows a max of 20–30 grams.
The vegans in the study at hand ate 15–20 more grams/day of fiber. High fiber intake is linked to better blood sugar control.
From the study abstract:
After correcting for age, gender, BMI at baseline, and physical activity, there was a significantly greater reduction in the primary outcomes fasting blood glucose and after-meal glucose in those patients receiving the Ma-Pi 2 diet compared with those receiving the control diet [low-fat]. Statistically significantly greater reductions in the secondary outcomes, HbA1c, insulin resistance, total cholesterol, LDL cholesterol and LDL/HDL ratio, BMI, body weight, waist and hip circumference were also found in the Ma-Pi 2 diet group compared with the control diet group. The latter group had a significantly greater reduction of triglycerides compared with the Ma-Pi 2 diet group.
The take-home point for me is that overweight T2 diabetics can improve short-term diabetes numbers despite a high carbohydrate consumption if they restrict calories and eat the “right” carbs. Restrict calories enough—600/day?—and T2 diabetes might be curable.
I’ve written before about vegetarian/vegan diets for diabetes. My patients are more resistant to vegan diets than they are to low-carb.
Not allowed not on the Ma-Pi 2 diet. Bacon, eggs, black coffee, and Cholula hot sauce.
I scanned the original report and don’t see any problems with Evelyn’s summary.
Diabetic Mediterranean Diet 
I don’t buy any study looking at those endpoints, especially A1c, lasting only three weeks.
Yeah, I’m not familiar with the calculated or estimated HgbA1c mentioned. Fructosamine would have been a good test for a 3-week study.