Measuring Shannon's diffusion
One way is to look at how many bits of the outputs are modified if you modify, say $t$ bits in the input. Actually, a function from $\{0,1\}^n$ to $\{0,1\}^m$ such that modifying $t$ bits in input modifies $m-t+1$ bits of output is said to achieve perfect diffusion.

Examples of functions with good diffusion are those associated with MDS matrices. For instance, the permutation layer of the AES is made of one such function (it is the "mixcolumn" part of the algorithm).