Live diesel refers to any scale model locomotive that is powered just as full sized diesel electrics are powered. That is, a diesel engine powering a generator, which in turn powers traction motors.
The most common example is G-scale locomotive "conversions" that use single-cylinder diesel motors.
Wada Works Burlington Zephyr live diesel locomotives.
OS 40 FS Engines Mounted in a Gauge 1 Garden Locomotive: Diesel Electric
Jerry Hyde of Hyde-Out Mountain Live Steam Live Diesel Electric model locomotive NP F7, followed by a British Class 66 live diesel. You MUST watch the Class 66 at 2:47 in the video push a brick sitting on the track! And watch out for a special live-steam treat at the end of the video.