  The late-time distribution function P(x,t) of a particle diffusing in a
one-dimensional logarithmic potential is calculated for arbitrary initial
conditions. We find a scaling solution with three surprising features: (i) the
solution is given by two distinct scaling forms, corresponding to a diffusive
(x ~ t^(1/2)) and a subdiffusive (x ~ t^{\gamma} with a given {\gamma} < 1/2)
length scale, respectively, (ii) the overall scaling function is selected by
the initial condition, and (iii) depending on the tail of the initial
condition, the scaling exponent which characterizes the scaling function is
found to exhibit a transition from a continuously varying to a fixed value.
