Picosecond pulse amplification in modulated amplifiers is demonstrated with negligible pulse distortion for modulation frequencies between 1 and 4 GHz. Existing measurements show that up to 2.5 GHz modulation can be achieved with a gate 'on' time of 200 ps. A numerical model is reported which simulates the behavior of diode laser amplifiers under RF current modulation and is shown to be in good agreement with experimental demonstration. A simple analytical model is also reported to indicate the physical causes in observed operating trends. It is shown that in optimized bulk devices, good modulation depth could potentially be achieved with a 100 ps gate 'on' time at 5 GHz modulation frequency.