It has been shown that the edge structure of the characteristic imset polytope is closely connected to the question of causal discovery. The diameter of a polytope is an indicator of how connected the polytope is and moreover gives us a hypothetical worst case scenario for an edge-walk over the polytope. We present low-degree polynomial bounds on the diameter of $\operatorname{CIM}_n$ and, for any given undirected graph $G$, the face $\operatorname{CIM}_G$.