Summary: Porous materials such as sedimentary rocks often show a fractal character at certain length scales. Deterministic fractal generators, iterated upto several stages and then repeated periodically, provide a realistic model for such systems. On the fractal, diffusion is anomalous, and obeys the law \(\langle r^2\rangle\sim t^{2/d_w}\), where \(\langle r^2\rangle\) is the mean square distance covered in time \(t\) and \(d_w>2\) is the random walk dimension. The question is: How is the macroscopic diffusivity related to the characteristics of the small scale fractal structure, which is hidden in the large-scale homogeneous material? In particular, do structures with same \(d_w\) necessarily lead to the same diffusion coefficient at the same iteration stage? The present paper tries to shed some light on these questions.