Accurately and precisely characterizing the morphology of small pulmonary structures from Computed Tomography (CT) images, such as airways and vessels, is becoming of great importance for diagnosis of pulmonary diseases. The smaller conducting airways are the major site of increased airflow resistance in chronic obstructive pulmonary disease (COPD), while accurately sizing vessels can help identify arterial and venous changes in lung regions that may determine future disorders. However, traditional methods are often limited due to image resolution and artifacts. We propose a Convolutional Neural Regressor (CNR) that provides cross-sectional measurement of airway lumen, airway wall thickness, and vessel radius. CNR is trained with data created by a generative model of synthetic structures which is used in combination with Simulated and Unsupervised Generative Adversarial Network (SimGAN) to create simulated and refined airways and vessels with known ground-truth. For validation, we first use synthetically generated airways and vessels produced by the proposed generative model to compute the relative error and directly evaluate the accuracy of CNR in comparison with traditional methods. Then, in-vivo validation is performed by analyzing the association between the percentage of the predicted forced expiratory volume in one second (FEV1\%) and the value of the Pi10 parameter, two well-known measures of lung function and airway disease, for airways. For vessels, we assess the correlation between our estimate of the small-vessel blood volume and the lungs' diffusing capacity for carbon monoxide (DLCO). The results demonstrate that Convolutional Neural Networks (CNNs) provide a promising direction for accurately measuring vessels and airways on chest CT images with physiological correlates.