Transient magnetic diffusion through conductors of thickness comparable to the skin depth is investigated. Since an analytical solution is unavailable in this case, such magnetic diffusion results must be determined via simulation or experimentation. In the experimental approach, a sinusoidal current with peak values in the range of 20-30 kA (approx. 7 kHz ringing frequency) is passed through a two turn coil generating a sinusoidally varying magnetic field. A hollow structure with metallic walls of controlled thickness is placed roughly 10 cm away from the exciting coil. The focus of this investigation is on the transient skin depth, which occurs during the first half-wave of the signal, as that is most relevant for pulsed power applications. A calibrated B-dot probe placed inside the structure facilitates measurement of the diffused field. As expected, experimental data shows that magnetic field diffusion through the wall is not instantaneous, causing a delay before the diffused field is measured inside the test structure. The impact of cracks and holes in the conductor on the speed and magnitude of the magnetic field diffusion is elucidated. Results for materials of different conductivities are compared and analyzed for the transition between thin and medium walled cases. FEM simulations are validated alongside these experimental results and used to access a larger parameter space.