Topological insulating phases are usually found in periodic lattices stemming from collective resonant effects, and it may thus be expected that similar features may be prohibited in thermal diffusion, given its purely dissipative and largely incoherent nature. We report the diffusion-based topological states supported by spatiotemporally-modulated advections stacked over a fluidic surface, thereby imitating a periodic propagating potential in effective thermal lattices. We observe edge and bulk states within purely nontrivial and trivial lattices, respectively. At interfaces between these two types of lattices, the diffusive system exhibits interface states, manifesting inhomogeneous thermal properties on the fluidic surface. Our findings establish a framework for topological diffusion and thermal edge/bulk states, and it may empower a distinct mechanism for flexible manipulation of robust heat and mass transfer.
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