From DAN:

Diving Medicine FAQs
Asthma and Scuba Diving

Q: My daughter has asthma, but it is controlled by medication. Can she learn to dive safely?

A:

In general, asthma is a lung disorder in which there is a tendency for the muscle surrounding the bronchi (breathing tubes) to contract excessively, causing narrowing, or broncho-constriction. As a result, this causes increased breathing resistance, which can manifest as wheezing, chest "tightness", cough, or breathlessness. In asthmatics, broncho-constriction can be precipitated by exposure to allergens, noxious fumes, cold air, exercise or respiratory infections such as a "cold". People with asthma may experience broncho-constriction due to more than one of these factors, but many asthmatics will experience a measurable increase in breathing resistance after exposure to any one or several of them. The increase in breathing resistance caused by bronchial narrowing may be compounded by the accumulation of mucus within the airways.

Serious potential risks may make scuba diving, which is often performed in isolated locations and far from competent medical care, an unwise elective sport for an individual with asthma. There are primarily two issues.

1. During scuba diving the diver experiences a reduction in breathing capacity due to the effects of immersion and an increase in breathing resistance caused by the higher gas density at depth. At 33-feet underwater, the maximum breathing capacity of a normal scuba diver is only 70-percent of the surface value. At 100-feet underwater, this reduction is approximately 50-percent. If, for example, a diver’s breathing capacity is already reduced because of asthma, there may not be sufficient reserve to accommodate the required increase demanded by exertion.
2. Both narrowing of the bronchi and excessive mucus production can inhibit exhalation of air during ascent, and could predispose the diver to pulmonary barotrauma leading to pneumothorax, pneumo-mediastinum and/or arterial gas embolism.

For these reasons, physicians trained in diving medicine have traditionally recommended that people with asthma should never dive. However, a consensus of experts at a 1995 workshop held under the auspices of the Undersea and Hyperbaric Medical Society (UHMS) proposed more liberal guidelines. Essentially, the UHMS workshop panel felt that the risk of diving is probably acceptable if, the diving candidate with some asthmatic ‘history’ demonstrates normal pulmonary function at rest (FVC, mid-expiratory flow, FEV1, FEF 25-75) and then again after strenuous exercise. It was also concluded that the degree of competency in making a medical assessment of diving fitness is enhanced if the examining doctor has relevant knowledge or experience of the diving environment and its associated hazards.

It is important to note that asthma severity can wax and wane. Symptoms may worsen for 4-6 weeks after a "cold" or during certain seasons (for example in response to high levels of pollen in the air.) Therefore, even if a person with asthma fulfills the criteria listed above, diving is not recommended unless the diver is free of respiratory symptoms before each dive.

Reference:

Elliott, D.H. (1996) Are Asthmatics Fit To Dive?, Undersea and Hyperbaric Medical Society (UHMS) – Annual Scientific Meeting, 21-June-1995

Additional Resources:
Read a more detailed article on asthma.