This effect appears like a paradox, as dry soil makes a very bad water conductor. Two effects prevent water from infiltrating:
- Air in the soil pores cannot escape: dry soil includes lots of air bubbles in small to large pores. If you expect water to get in, how do you think the air could get out? Often it gets stuck, and no water can infiltrate anymore. This effect also leads to dangerous flash-floods even during droughts, when strong rain events hit super-dry soil.
- Sticky capillary forces: Water forms droplets and becomes sticky due to surface tension when in contact with lots of air. The effect is even stronger in smaller pores. So it is very hard for water to create a flowing stream.
Under these circumstances, water cannot simply diffuse, because random walk is hindered by air bubbles and capillary forces. As soon as the soil is saturated, water and solutes can actually diffuse. As a consequence, water flows faster in wet soil, since it can develop a continuous stream.
The dashed line in the graph below expresses this fact by showing the hydraulic conductivity (i.e. how fast water infiltrates) as a function of soil moisture (from dry to wet).
--- EDIT: The actual behaviour of water infiltration is a superposition of the two effects described above. Very dry soil is often compacted and therefore exhibits small pores. Small pores cannot absorb huge amounts of water quickly enough, because (1) the only path for the air to escape is upwards, which is where the rainfall water influx is sustaining a surface cover, and (2) water is hesitant to fill the pores since capillary counterforces are inversally related to pore radius. One might argue that air bubbles can still rise in water, but in a small-pore domain, bubble formation and uprising is slow and inefficient. Eventually, this tragedy can lead to flash floods.