The present investigation deals with the propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, thin elastic plate of finite width, in the context of generalized theory of thermoelastic diffusion. Lord and Shulman(L-S) theory, in which thermal and thermo-mechanical relaxation is governed by a time constant and diffusion relaxation is governed by other different time constant, is selected for the study. According to the characteristic equation, three quasi-longitudinal waves, namely: quasi-elastodiffusive(QED-mode), quasi-massdiffusive(QMD-mode) and quasi-thermodiffusive(QTD-mode), can propagate in addition to quasi-transverse waves(QSV-mode), and the purely quasi-transverse motion(QSH-mode), which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew-symmetric modes of the plate are derived. The amplitudes of displacements, temperature change and concentration for symmetric and skew-symmetric modes of vibration of plate are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient and amplitudes of wave propagation, are presented graphically in order to illustrate and compare the analytical results. Some special cases of frequency equation are also deduced from the present investigation.