  The relationship between the microstructure of a porous medium and the
observed flow distribution is still a puzzle. We resolve it with an analytical
model, where the local correlations between adjacent pores, which determine the
distribution of flows propagated from one pore downstream, predict the flow
distribution. Numerical simulations of a two-dimensional porous medium verify
the model and clearly show the transition of flow distributions from
$\delta$-function-like via Gaussians to exponential with increasing disorder.
Comparison to experimental data further verifies our numerical approach.
