Pulmonary Fibrosis has been linked to Sleep Apnea, a breathing problem that occurs during sleep and known to contribute to microscopic lung tissue injury. We believe that this microscopic lung tissue injury heals with scar tissue in some people, leading to Pulmonary Fibrosis. Our project is a clinical trial of CPAP -- a standard treatment for Sleep Apnea -- to treat IPF. We hope to find out if we can reduce microscopic lung tissue injury in IPF and also decrease the tendency of lung tissue to scar, improve lung function and oxygen levels, relieve shortness of breath, and make people feel better.