It seems to me like it should, but I don't think I've seen it stated plain and simple. What I have found is in Acrobatics:
You can keep your balance while traversing narrow or treacherous surfaces.
Is Difficult Terrain "treacherous"? Mh...
You can use Acrobatics to move on narrow surfaces and uneven ground without falling.
Is Difficult Terrain "uneven ground"? Mh...
If I look at the Table:
Surface Width: Greater than 3 feet wide => Base Acrobatics DC: 0*
* No Acrobatics check is needed to move across these surfaces unless the modifiers to the surface (below) increase the DC to 10 or higher.
So let's look at the modifiers:
Slightly obstructed (gravel, sand) +2
Severely obstructed (cavern, rubble) +5
Move at full speed on narrow or uneven surfaces +5
Based on this, am I right to say that one can make an Acrobatics check against DC 10 (severely obstructed + full speed) to move at full speed through difficult terrain?