square meter per second

Anything that spreads by random molecular wandering rather than by being carried along has a diffusivity, and diffusivity always carries units of area per time. That is not a coincidence: the diffusion equation $\partial T/\partial t = \alpha \nabla^2 T$ needs $\alpha$ to reconcile a second spatial derivative with a first time derivative. The practical consequence is the square-root rule. A diffusive front travels a distance of roughly $\sqrt{\alpha t}$, so covering twice the distance takes four times as long. This is why a thick steel plate takes disproportionately longer to heat through than a thin one, and why diffusion is hopeless as a transport mechanism over any large distance.

Some values for scale, all in m²/s: copper's thermal diffusivity is about 1.1 × 10⁻⁴, air about 2.2 × 10⁻⁵, water about 1.4 × 10⁻⁷, and brick or concrete around 5 × 10⁻⁷. Copper spreads heat nearly a thousand times faster than water, which is why saucepans have copper bases and why thermal mass in a building is measured in hours of lag rather than seconds. Note that high conductivity and high diffusivity are not the same thing: diffusivity is conductivity divided by volumetric heat capacity, so a material can conduct well and still respond slowly if it stores a lot of heat per degree.