Deep observation of the High Energy Stereoscopic System (HESS) on the most extended pulsar wind nebula HESS J1825-137 reveals an enhanced energy-dependent morphology, providing useful information on the particle transport mechanism in the nebula. We find that the energy-dependent morphology is consistent with a diffusion-dominated transport of electrons/positrons. It provides an alternative possible interpretation for the unusually large spatial extent (i.e., $gtrsim 100$pc) of the nebula, which could then be attributed to the diffusion of escaping electrons/positrons from a compact plerion. The influence of various model parameters on the energy-dependent extent of the nebula is studied in the diffusion-dominated scenario. We also show that the energy-dependent morphology of the nebula may also be used to study the spin-down history of the pulsar.
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