I understand what SP-network (Substitution-Permutation Network) and Feistel Network look like. And those ciphers based on Feistel (e.g. DES) often achieve so called E/D similarity, which indicates that the cipher itself follows the same pattern during either encryption or decryption.
SPN, comparing with Feistel Network, can bring more "confusion" into the cipher indeed. But the ciphers deriving from SPN (e.g. AES) may not be able to realize this E/D similarity. For instance, we have to put the inverse SBOX into the AES decryption process.
Thus, can we design a block cipher based on SP-network without loss of E/D similarity theoretically? Thanks!