  We explore the spatio-temporal evolution of solar flares by fitting a radial
expansion model $r(t)$ that consists of an exponentially growing acceleration
phase, followed by a deceleration phase that is parameterized by the
generalized diffusion function $r(t) \propto \kappa (t-t_1)^{\beta/2}$, which
includes the logistic growth limit ($\beta=0$), sub-diffusion ($\beta = 0-1$),
classical diffusion ($\beta=1$), super-diffusion ($\beta = 1-2$), and the
linear expansion limit ($\beta=2$). We analyze all M and X-class flares
observed with GOES and AIA/SDO during the first two years of the SDO mission,
amounting to 155 events. We find that most flares operate in the sub-diffusive
regime ($\beta=0.53\pm0.27$), which we interpret in terms of anisotropic chain
reactions of intermittent magnetic reconnection episodes in a low
plasma-$\beta$ corona. We find a mean propagation speed of $v=15\pm12$ km
s$^{-1}$, with maximum speeds of $v_{max}=80 \pm 85$ km s$^{-1}$ per flare,
which is substantially slower than the sonic speeds expected for thermal
diffusion of flare plasmas. The diffusive characteristics established here (for
the first time for solar flares) is consistent with the fractal-diffusive
self-organized criticality (FD-SOC) model, which predicted diffusive transport
merely based on cellular automaton simulations.
