Several long term studies show multiple signs of improvement on a whole foods vegan diet.

Bone samples taken from early Roman gladiators indicate that they were fed a plant-based diet like barley and beans. [The Game Changers]
In fact, several long term population studies show that groups who were mostly on a vegan diet had better health indicators than other groups:
- 16% less cancer
- 15% lower mortality
- 63% lower incidence of hypertension
- 62-78% less diabetes risk
- 10% less heart disease
- 10% less hypothyroidism
- a normal BMI
You cannot eat large amounts of processed vegan junk food and expect all of these results. But if you take the equivalent healthiness of an omnivorous diet and shift over to a vegan diet with the same proportion of processed foods, you will see an improvement. The claims above are based off the population studies of vegans who eat a standard vegan diet which includes processed foods and still see massive benefits. [Critical Reviews in Food Science and Nutrition, JAMA Internal Medicine, NMCD, Nutrients, American Journal of Clinical Nutrition]
An interview of identical twins, Hugo and Ross Turner, one of whom goes vegan and one stays omnivorous.