Participants with heart failure with preserved ejection fraction will undergo 12 weeks of cardiac rehabilitation for exercise training (ET) and be randomized to either nebulized sodium nitrite inhalation solution or placebo inhalation solution (normal saline) through the training period. Study drug is administered 3 times daily during daytime hours with one of these doses being immediately prior to onset of ET sessions throughout the 12 week trial. The objective is to determine if the inhaled sodium nitrite improves the clinical responses and tolerability of ET.