If we have two points that "randomly" move either a unit closer together or a unit further apart and we accumulate these motions over time, these points allows appear statistically to be moving apart.

If we're at a distance d(t) at time, t and the next change is to either d(t+1)=d(t)+1 or d(t+1)=d(t)-1 with 50/50 probability, in terms of the average squared distance (root mean square), this becomes a statistical constant velocity:

d(t+1)^2=((d(t)+1)^2+(d(t)-1)^2)/2
d(t+1)^2=((d(t)^2+2d(t)+1)+(d(t)^2-2d(t)+1))/2
d(t+1)^2=(2d(t)^2+2)/2
d(t+1)^2=d(t)^2+1

This apparent constant velocity motion is also true of diffusion in any number of dimensions.

An object undergoing coherent motion in a single direction then appears to (de)accelerate parabolically relative to this.

There are better ways of looking at motion though ...