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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. greater than or similar to 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.