Accurate motion estimation in thoracic computed tomography (CT) plays a crucial role in the diagnosis and treatment planning of lung cancer. This paper provides two key contributions to this motion estimation. First,we show we can effectively transform a CT image of effective linear attenuation coefficients to act as a density,i.e. exhibiting conservation of mass while undergoing a deformation. Second,we propose a method for diffeomorphic density registration for thoracic CT images. This algorithm uses the appropriate density action of the diffeomorphism group while offering a weighted penalty on local tissue compressibility. This algorithm appropriately models highly compressible areas of the body (such as the lungs) and incompressible areas (such as surrounding soft tissue and bones).