  Parity and time invariance violating (${\cal P},{\cal T}$-odd) nuclear forces
produce ${\cal P},{\cal T}$-odd nuclear moments, for example, the nuclear
Schiff moment. In turn, this moment can induce electric dipole moments (EDMs)
in atoms. We estimate the contribution to the Schiff moment from the soft
collective octupole vibrations existing in many heavy nuclei. Two possible
mechanisms are considered, mixing of the ground state of an odd-$A$ nucleus
with the octupole phonon state, and ${\cal P},{\cal T}$-odd admixture to the
single-particle wave function of the valence nucleon. We found practically the
same contribution to the Schiff moment as that of the static octupole
deformation calculated earlier. This confirms a suggestion that the soft
octupole vibrations can replace the (controversial) static octupoles in
development of the collective Schiff moments. The values of atomic EDM
predicted for $^{223,225}$Ra and $^{223}$Rn are enhanced by factors up to
$10^{3}$ compared to experimentally studied spherical nuclei $^{199}$Hg and
$^{129}$Xe.
