I have been trying with Diaphragmatic breathing for some time. As i see, it doesn't affect directly my speech but it influences my way of speech in a way around. I was once told by a speech therapist that "excitement is the main cause of stuttering". I found it true to a good extent because when i undergo excitement or similar emotions, its more hard to control the speech.
It takes more time to do a Diaphragmatic Breath when compared to a nose to chest breath. In the process, it calms one down and also asks to speak slowly, inorder to match with the slow rhythm of the breath.
Also, the power to make sounds actually comes from the exhalation of air. The more air you have in your stock, the more time you can produce speech without going for the next inhalation.