Bad breath can be caused by a dry mouth. When you eat less, your body produces less saliva, and since saliva helps keep your mouth clean its absence can create a bacteria-friendly environment. In your pie hole.

I remember reading somewhere that when your body starts to break down its fat stores, your digestive system produces an odor that comes out in the breath...but I don't know how true that is or what part of the process could cause that reaction.

So, drink a lot of water to keep your mouth hydrated (or maybe chew sugar-free gum?). If it actually is true that your body is metabolizing fat and that's what's causing the odor, maybe your diet is working!