I don't think you can directly extrapolate the benefits of warming up in other sports to scuba diving. Diving is unique in that there is DCS risk.
Read
Doc Vikingo's article on exercise and diving. It's a nice summary of some of the recent scientific studies on the subject.
If you review the scientific literature, you'll see a few studies that investigate the effects of pre-dive and post-dive exercise on Doppler-detected venous gas emboli in divers. Although the results are not quite conclusive (at least one dissenting study) and they exclusively look at "strenuous" exercise, they suggest that there may be some increased DCS risk in exercising within 4-6 hours of beginning a dive. Based on these findings, the prevailing opinion regarding DCS risk for recreational no-deco dives is that strenuous exercise occurring 12-24 hrs before the dive is protective, strenuous exercise 4-6 hrs before the dive is probably harmful, and exercise 6-24 hrs post-dive may be harmful given a high nitrogen load. One possible explanation for the "bad" pre-dive interval is that vigorous musculoskeletal activity expands the population of micronuclei which persist for approx. 2-5 hrs. That's a bad thing to do right before a dive. Admittedly, our knowledge about all of this stuff is far from complete.
The theoretical danger to a diver who "warms up" before a dive is that he may exercise too vigorously, pump up the number of micronuclei and, in so doing, increase his DCS risk. For this reason, it might be better just to do some light stretching (to prevent muscle pulls), restrict activity to very light exercise (walking, moving gear around, etc.) and relax a little before the dive.
On a related note, some studies have looked at the effect of aerobic fitness on intravascular bubble formation in divers. The consensus appears to be that a diver accustomed to a higher of physical activity (aerobically fit) will have fewer bubbles than a diver with lower activity, all other things being equal.
Synthesizing this and other info...
In order to minimize DCS risk, the scuba diver should be a physically fit individual who exercises regularly, paying particular attention to aerobic exercise. He should exercise about 12-24 hrs before a dive to access the "protective" effect (nitric oxide mechanism?), avoid vigorous activity leading up to the dive, minimize activity during the bottom nitrogen-loading phase, conduct light exercise during the ascent phase, and avoid strenuous physical activity up to 24 hours post-dive.
If divers are maintaining a healthy level of physical activity and aerobic fitness, scuba diving really should be on the "less physically demanding" end of the work-out spectrum. Unfortunately, I suspect that, for many divers, that isn't the case.