  Diffusion is one of the most ubiquitous transport phenomena in nature.
Experimentally, it can be tracked by following point spreading in space and
time. Here, we introduce a spatiotemporal pump-probe microscopy technique that
exploits the residual spatial temperature profile obtained through the
transient reflectivity when probe pulses arrive before pump pulses. This
corresponds to an effective pump-probe time delay of 13 ns, determined by the
repetition rate of our laser system (76 MHz). This pre-time-zero technique
enables probing the diffusion of long-lived excitations created by previous
pump pulses with nanometer accuracy, and is particularly powerful for following
in-plane heat diffusion in thin films. In contrast to existing techniques for
quantifying thermal transport it does not require any material input parameters
or strong heating. We demonstrate the direct determination of the thermal
diffusivities of the layered materials MoSe$_2$ (0.18 cm$^2$/s), WSe$_2$ (0.20
cm$^2$/s), MoS$_2$ (0.35 cm$^2$/s), and WS$_2$ (0.59 cm$^2$/s). This technique
paves the way for observing novel nanoscale thermal transport phenomena and
tracking diffusion of a broad range of species.
