Diabetes comes in two types, Type 1 and Type 2. While there is some evidence that genes have something to do with developing either type of diabetes, the jury is still out on this issue. That is, if both your parents have it, there is a chance (how much of a chance is still being debated) that you will also have it. But this is mostly because you may share many of your parents' habits and attitudes about diet, exercise, and lifestyle, not necessarily because of your genes.
The best way to prevent Type 2 diabetes is to maintain a healthy weight AND body fat percent. This is because excess fat can lead to impaired uptake of glucose (sugar) by the body, which then leads to diabetes. However, having a healthy weight is not enough. Your weight should be a good proportion of muscle mass to bone mass to fat mass. You can be in a healthy weight range but have an unhealthy fat percent for your body. Likewise, plenty of people are in a healthy weight range (and they even look fabulous), but their arteries are clogged.
Basically, any exercise regimen that keeps you at a healthy weight with a good balance of body masses is good enough to prevent Type 2 diabetes.
As for Type 1 diabetes... This is known as "juvenile" diabetes because the usual age of onset is very young. In Type 1 diabetes, the pancreas ceases to work (again, the reasons are many and not well understood). This prevents the pancreas from producing insulin, eventually leading to the poor absorption of glucose by the body. For Type 1 diabetes, exercise can help keep you healthy, but no amount of exercise can make the pancreas work again.