  We elucidate that the diffusive systems, which are widely found in nature,
can be a new platform of the bulk-edge correspondence, a representative
topological phenomenon. Using a discretized diffusion equation, we demonstrate
the emergence of robust edge states protected by the winding number for one-
and two-dimensional systems. These topological edge states can be
experimentally accessible by measuring the diffusive dynamics at the edges.
Furthermore, we discover a novel diffusive phenomenon by numerically simulating
the distribution of temperatures for a honeycomb lattice system; the
temperature field with wavenumber $\pi$ cannot diffuse to the bulk, which is
attributed to the complete localization of the edge state.
