Diets have been (anecdotally at least) shown to be effective in the treatment of autoimmune diseases like Type 1 diabetes, multiple sclerosis, Chron's disease, and many others. A popular book on the subject is The Wahl's Protocol: https://www.amazon.com/Wahls-Protocol-Autoimmune-Conditions-...

Now, that's mostly anecdotal. There are very few studies on diet in general. As far as type 2 diabetes is concerned, though, low-carb diets have empirically been shown to reduce the need for insulin injections, slow progression of disease, and prevent the disease in the first place.

you can reduce your need for insulin with diet, but no it's not possible to fully cure. but with monitoring and an a needle to hand it's pretty close.