If DO2 is sufficiently low (e.g., at rest, less than 1/3 normal), the diffusion of O2 from alveoli into pulmonary capillary blood will be so slow that the capillary blood will not have time to equilibrate with alveolar gas during its passage through the capillaries. Therefore, pulmonary venous blood will have a lower PO2 than that of alveolar gas, so systemic arterial blood, which is supplied by the pulmonary veins, will be low also.
Example: pulmonary edema
Note: The problem of low D-O2 will be more severe in exercise, when the blood has less time in pulmonary capillaries to equilibrate with alveolar gas.