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Topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and is widely observed for electromagnetic and acoustic waves. Here, the notion of band topology is extended from wave to diffusion dynamics. Unlike wave systems that are usually Hermitian, diffusion systems are anti‐Hermitian with purely imaginary eigenvalues corresponding to decay rates. By direct probe of the temperature diffusion, the Hamiltonian of a thermal lattice is experimentally retrieved, and the emergence of topological edge decays is observed within the gap of bulk decays. The results of this work show that such edge states exhibit robust decay rates, which are topologically protected against disorder. This work constitutes a thermal analogue of topological insulators and paves the way to exploring defect‐immune heat dissipation.

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Non‐Hermiticity may significantly influence the topology of a photonic/electronic lattice, giving rise to point gaps, which have attracted much attention in recent years. While the influences of the point‐gap topology on the bulk‐boundary correspondence for the line gap have been widely studied, the topological lattice that simultaneously processes the line‐gap and point‐gap topological transitions has not been reported. Here, a strategy to simultaneously manipulate the line‐gap and point‐gap topologies in non‐Hermitian lattices is proposed. By introducing the asymmetric intercell coupling, the line‐gap topological transition process is demonstrated. By further considering the nonreciprocal coupling between the nearest neighboring unit cells, the point‐gap and line‐gap topological transitions can be simultaneously realized. Finally, the influence of the next nearest coupling on non‐Hermitian line‐gap and point‐gap topologies is also discussed.