Analysis of CT scans for studying Chronic Obstructive Pulmonary Disease (COPD) is generally limited to mean scores of disease extent. However, the evolution of local pulmonary damage may vary between patients with discordant effects on lung physiology. This limits the explanatory power of mean values in clinical studies. We present local disease and deformation distributions to address this limitation. The disease distribution aims to quantify two aspects of parenchymal damage: locally diffuse/dense disease and global homogeneity/heterogeneity. The deformation distribution links parenchymal damage to local volume change. These distributions are exploited to quantify inter-patient differences. We used manifold learning to model variations of these distributions in 743 patients from the COPDGene study. We applied manifold fusion to combine distinct aspects of COPD into a single model. We demonstrated the utility of the distributions by comparing associations between learned embeddings and measures of severity. We also illustrated the potential to identify trajectories of disease progression in a manifold space of COPD.