Pulmonary perfusion is spatially correlated with neighboring regions of lung having similar magnitudes of flow and distant pieces exhibiting negative correlation. Although local correlation has been noted in a wide variety of natural processes, negative correlation has not and it may be unique to organ blood flow. We investigate the regional perfusion predicted by a three-dimensional branching vascular model to determine whether such a model can create negative correlation of perfusion. The distribution of flows is modeled by a dichotomously branching tree in which the fraction of flow from parent to daughter branches is gamma and 1-gamma at each bifurcation. The flow asymmetry parameter (gamma) is randomly chosen for each bifurcation from a normal distribution with a mean of 0.5 with an SD of sigma. The branches branch along one of three orthogonal directions to assure a space-filling structure. This model produces flow distributions similar to those observed in experimental animals, with perfusion being positively correlated locally and negatively correlated at distance. The model is refined by incorporating an effect of gravity, which redirects a fraction (delta), of the flow against gravity to the companion daughter branch in the gravitational direction. A flow bias in the "dorsal" direction is also introduced to account for differences in supine-prone perfusion gradients. In its final form, this three-dimensional branching model accounts for previously observed 1) spatial correlation of regional perfusion with negative correlation over distance, 2) isogravitational perfusion heterogeneity, 3) differences in supine and prone perfusion gradients, 4) positive correlation of flows between supine and prone postures, 5) relatively small contributions of gravity to perfusion heterogeneity, and 6) fractal distributions of flow. This three-dimensional branching vascular model relates the function and structure of the pulmonary vascular tree, offering an explanation for both heterogeneous and spatially correlated regional flows.