"Disease" is such a broad category that it's sort of meaningless here.
Maybe veganism is healthier than an animal diet, but the degree of its impact can only be stated only after removing the many other environmental factors that might be contributing to lower disease rates among vegans, including income and location.
I find it interesting though that the right type of vegan diet will basically make you hypertension and heart attack proof and that it may also reverse heard disease (the only diet to do so). Especially when you look at mortality and costs of healthcare this really need to be more generally recognized.
A diet making someone heart-attack-proof is a pretty strong claim. Have a citation?
I think the only thing one can say with near-certainty about a well balanced vegan diet is that it has much lower environmental externalities (i.e carbon footprint, water usage) than a meat-based diet, while being no worse for you than any other comparably healthy diet.
That alone is a great reason to be a vegan, without having to rely on possibly hyperbolic claims of health benefits.