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A fundamental understanding of unusual atomic dynamics and collective modes in superionic conductors has been of great importance in improving renewable energy technologies such as thermoelectric energy conversion and electrolytes for rechargeable batteries. Herein, we have performed an in-depth study of the lattice dynamics evolution across the superionic transition of KAg₃Se₂ by analyzing the thermally driven density fluctuations. We show that the diffuson-like phonons induced by the strong anharmonicity of Ag sublattice dominate thermal transport below the superionic transition, resulting in ultralow lattice thermal conductivity in the normal ordered state. We find that the contributions of convection and conduction-convection interactions to lattice thermal conductivity increase significantly due to the liquid-like flow of Ag atoms. We further demonstrate that the dynamic disorder is too slow to completely suppress the propagating of long-wavelength transverse phonons in the superionic state of KAg₃Se₂, while the Ag-dominated short-wavelength transverse phonons near the Brillouin zone boundary break down. These results provide new physical insights into the complex atomic dynamics of superionic conductors.