I believe that breathing diaphragmatically during exercise, is a great breathing retraining activity that strengthens cardiac muscle and the muscles of respiration. Try taking a short jog focusing on the sensations you feel when alternating between inhalations and exhalations. You are likely alternating far too quickly. Try blowing nearly all the way out, and breathing nearly all the way in with each breath. This creates an intense even uncomfortable feeling, and ironically many people breathe shallowly while exercising because they are concerned that they will not get enough air if they were to breathe deeply. As long as you are breathing heavily, you are getting plenty of oxygen. I think that it is especially helpful to breathe diaphragmatically when the heartrate is elevated because it is the sensation of elevated heart rate that makes you want to alternate prematurely between inhalation and exhalation. Your heartbeat begins to hurt, sending you signals to breathe shallowly. Ignore the panic signals from your heart, and ensure that you breathe all the way in and out near full capacity. To do this you have to fight to resist the reflexes in your chest that prematurely interrupt a full exhalation.
Diaphragmatic breathing during exercise produces the same discomfort that diaphragmatic breathing at rest produces, just highly amplified. As long as you stay calm and keep breathing diaphragmatically you will habituate to this discomfort and learn to breathe more deeply and evenly. I believe that when you feel your heart beating hard in your chest and you keep blowing out, that is when you are doing the most good, you are restructuring your unhealthy breathing patterns and demolishing the trauma that underlies them. Endurance athletes usually have the lowest resting heart rates, I believe this is because they naturally learn to breathe diaphragmatically during exercise.
Activity: Take a 5 minute jog extending your inhalations and exhalations, focusing on the effort involved and the accompanying sensations. Instead of panting at a rate of multiple inhalations per second try to breathe in for 1 to 3 seconds and breathe out for 2 to 4 seconds.