A reduction in drag will result if the longitudinal component of pressure drag on the diffuser face is less than the diffuser exit area times the pressure that would have existed without a diffuser. This is how a diffuser may be used to reduce overall drag.
Assuming the exit pressure of the diffusers are the same and exit velocity ~= freestream. Both diffusers have the same length. For two diffusers, one at a lower height than the other:
Neglecting viscous effects (assuming no bl separation or viscous drag) & 3d effects
cp = pressure coefficient
Higher DF (larger exit area or lower throat area) diffusers may result in increased overall drag because they must recover more pressure. For arguments sake, let's use ideal diffusers (no spanwise flow) with throat velocities 2 (high ride height) and 3 (low ride height) times freestream. Our cp_mins are -3 and -8, respectively. If the pressure is to be recovered linearly (a bold assumption) with the same diffuser angle, the drag is proportional to the area contained in the pressure recovery region of the cp vs chord graph which, in this case, is just a triangle. The proportion of drag is then (.5*(8-0)*diffuser length)/(.5*(3-0)*dl) = 8/3. Now to calculate the Cl and Cd, the diffuser angle is 10 deg, and the throat length is equal to the diffuser length.
Low DF diffuser:
Cd = 0.5*3*0.5*sin(10deg) = .13
Cl = 0.5*3+0.5*3*0.5*cos(10deg) = 2.24
L/D = 17
High DF diffuser:
Cd = 0.5*8*0.5*sin(10deg) = .35
Cl = 0.5*8+0.5*8*0.5*cos(10deg) = 6.0
L/D = 17
The assumptions are the reason the efficiencies match. Obviously a myriad of viscous and 3d effects prevents these numbers from being realistic. These unaccounted for effects largely serve to reduce the efficiency of higher df diffusers. (real max cl for any single element (single deck) wing/diffuser is ~3). Although the magnitude of these coefficients are off, their ratio (~20:1) is not unrealistic (nor does it take into account any reduction the diffuser may have on the body's drag) because diffusers don't really suffer from induced drag. The L/D for even an 'inefficient' diffuser is still much higher than a wing's efficiency, so it is almost always worthwhile to increase diffuser df.
I believe someone mentioned induced drag being a problem with diffusers: The reason diffusers are so efficient is they have very little induced drag because tip vortices cannot form due to the diffusers proximity to the ground. Run a calculation for induced drag with an underwing's AR (<0.5) and it will seem worthless. Example: CL = 1, AR = 0.5, e = 0.85 (rectangular wing e). CDi = 0.75, L/D = low. Clearly not worth running if induced drag is a problem.
DF can be created without a drag penalty but, as someone said before, you're unlikely to generate df without drag on a well designed aero package.