  We present a systematic study of particle transport by diffusion in young
pulsar wind nebulae (PWNe). We selected nine bright sources that are well
resolved with the Chandra X-ray Observatory. We analyzed archival data to
obtain their radial profiles of photon index ($\Gamma$) and surface brightness
($\Sigma$) in a consistent way. These profiles were then fit with a pure
diffusion model that was tested on Crab, 3C 58 and G21.5$-$0.9 before. In
addition to the spectral softening due to the diffusion, we calculated the
synchrotron power and built up the theoretical surface brightness profile. For
each source, we performed separate fits to the $\Gamma$ and the $\Sigma$
profiles. We found these two profiles of most PWNe are similar, except for Crab
and Vela. Both profiles can be well described by our model, suggesting that
diffusion dominates the particle transport in most sampled PWNe. The
discrepancy of parameters between the $\Gamma$ profile and $\Sigma$ profiles is
relatively large for 3C 58 and G54.1+0.3. This difference could be attributed
to the elongated shape, reflecting boundary, and the non-uniform magnetic
field. Finally, we found no significant correlations between diffusion
parameters and physical parameters of PWN and pulsar.
