Diesel is thinner than water, so will show evidence of a leak that is too small for water to pass through.
Air is thinner than diesel, so will show evidence of a leak that is too small for diesel to pass through.
Vacuum box testing of segmented areas is an option, but is highly susceptible to operator error and is very labor intensive.
Leak testing of large areas with air is far cheaper than with diesel.

When leak testing with air, you must be careful to avoid over pressurization, which will damage the structure and/or cause a violent explosion. All you need is about 2 psi.
A simple yet very safe air testing inlet and safety pressure relief mechanism is to attach a length of 2" pipe to the duct to be tested that is a foot or two long. The pipe will have a compressed air inlet connected to the side with a ball valve that acts as a simple pressure regulator,meant to throttle the release of the compressed air into the duct.
The end of the pipe will have a loose fitting slip fit plug that weighs about 2 pounds. When the pipe is installed in the vertical position, gravity keeps the 2 pound loose slip fitplug in place to seal the end of the pipe, until the internal pressure reaches about 2 psi. Then the loose slip fit plug will float in place when the internal pressure reaches about 2 psi. If too much air pressure is introduced, you'll blow the plug out and risk damaging, but not exploding, the duct. Regulate the incoming air flow until the plug floats just a bit from the end of the pipe.
This process does not provide and exact or chartable pressure, but simply and cheaply allows soap bubble testing of the duct or compartment exterior.

Unlike with diesel, this test method allows immediate, efficient weld repair of any found leaks. Simply shut off the air while the repair is being made, then restart the flow immediately after.

Also, this test needs to be completed prior to any coatings are applied to the welds. Any welds that have not been previously verified as leak free will need to have coatings removed prior to the leak testing.

Be warned that if this is not done correctly, serious damage/injury can result. Ensure that the method and it's application is pre- approved and inspected by all applicable engineering, supervision and safety department personnel. Do not attempt this unless you are positive that appropriate and redundant safety precautions are in place and you are willing to accept responsibility for the work.

I can't speak for the testing of duct work, but many years ago in the oil and gas industry the diesel test (which is a penetrating medium of sorts) was common for testing for leaks on storage tanks. I always used dye penetrant developer on the opposite face to detect any diesel that may find it's way through.  The downside is the clean-up.  Tim makes some excellent points about using a low pressure air test and a solution that will form bubbles such as soapy water, 409 cleaner, or a professional product like Bubble Up.