Topological physics has garnered attention across various fields, emphasizing topologically protected modes renowned for their robustness against disorders. Recent advancements have expanded from conservative wave systems to diffusion systems with dissipative interactions. However, the transition region between wave and diffusion dynamics remains scarce, primarily due to the complexities involved in coupling modulation. Here, we develop a universal coupling control scheme via reservoir engineering, achieving conservative, dissipative, and mixed topologies in an optical waveguide array. Contrary to the belief that topological modes are disorder resistant, we found that topological dissipative modes are highly sensitive to initial excitations and noise. This sensitivity is due to their residence within the complex band gap, facilitating the excitation and preservation of bulk modes with lower loss. We also propose a method to control the degree of topological robustness and even stabilize these sensitive topological states by selectively managing dissipative potentials. Our Letter offers new insights into the dissipative dynamics of topological states, paving the way for wave coherent manipulation and diffusion transport on photonic chips.

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• Edge states
• Integrated optics
• Topological effects in photonic systems
• Non-Hermitian systems
• Waveguide arrays