The Generalized Feistel Structure (GFS) generally uses the sub-block-wise cyclic shift in the permutation layer, the layer between the two
function layers. For Type 2 GFS, at FSE 2010, Suzaki and Minematsu showed that a better diffusion property can be obtained if one uses some other sub-block-wise permutation. In this paper, we consider Type 1, Source-Heavy (SH), and Target-Heavy (TH) GFSs, and study if their diffusion properties can be improved by changing the sub-block-wise cyclic shift. For Type 1 GFS, we show that it achieves better diffusion for many cases, while this is not the case for SH and TH GFSs, i.e., the diffusion property of SH and TH GFSs does not change even if we change the sub-block-wise cyclic shift. We also experimentally derive optimum permutations in terms of diffusion, and evaluate the security of the resulting schemes against saturation, impossible differential, differential, and linear attacks.