  Emission from carbon monoxide (CO) is ubiquitously used as a tracer of dense
star forming molecular clouds. There is, however, growing evidence that a
significant fraction of CO emission originates from diffuse molecular gas.
Quantifying the contribution of diffuse CO-emitting gas is vital for
understanding the relation between molecular gas and star formation. We examine
the Galactic distribution of two CO-emitting gas components, a high column
density component detected in 13CO and 12CO, and a low column density component
detected in 12CO, but not in 13CO. The "diffuse" and "dense" components are
identified using a combination of smoothing, masking, and erosion/dilation
procedures, making use of three large-scale 12CO and 13CO surveys of the Inner
and Outer Milky Way. The diffuse component, which globally represents 25
(1.5x1e8 Mo) of the total molecular gas mass (6.5x1e8 Mo), is more extended
perpendicular to the Galactic plane. The fraction of diffuse gas increases from
15% at a galactocentric radius of 3 kpc to 50% at 15 kpc, and increases with
decreasing surface density. In the Inner Galaxy, a yet denser component traced
by CS emission represents 14% of the total molecular gas mass traced by 12CO
emission. Only 14% of the molecular gas mass traced by 12CO emission is
identified as part of molecular clouds in 12CO surveys by cloud identification
algorithms. This study indicates that CO emission not only traces star forming
clouds, but also a significant diffuse molecular ISM component.
