Abstract: By comparing the similarity of diffusion equation and the Schrödinger equation, the paper addresses the time-reversal invariance of the physical equations. Although the diffusion of a quantum wavepacket exhibits the same characteristics as the classical particles, it is essentially different. The diffusive matter wave remains diffuse even though the time is reversed while the time-reversal invariance holds. As two wavepackets overlap, it reveals the phenomenon of interference.

Key words: diffusion equation, Schr?dinger equation, time-reversal symmetry, wavepacket interference