Ever heard of Breath Support? Think "Abs!" It's all about the abdominal muscles (or, more specifically, your Transversus - watch for a future post.)
Now... the reality is that it's not just about abs/transverse. It's also about the pelvic diaphragm, the internal intercostals, and other ab muscles - and they all work in conjunction with the diaphragm (and the external intercostals) to balance the air flow. The big mistake is to think that the diaphragm is sending the air out sufficiently for your voice to work optimally.