  For the first time, the energy diffusion approximation is confronted at the
percent level with the exact numerical modeling of thermal decay of a
metastable state. The latter is performed using the quasistationary decay rates
resulting from the Langevin equations for the coordinate and conjugated
momentum. For the energy (or action) diffusion approach, a Langevin-type
equation for the action is constructed, validated, and solved numerically. The
comparison of two approaches is performed for four potentials (two of which are
anharmonic) in a wide range of two dimensionless scaling parameters: the
governing parameter $G$ reflecting how high is the barrier with respect to the
temperature and the damping parameter $\varphi$ expressing the friction
strength. It turns out that the action diffusion approach produces the rate
which is in 50% agreement with the exact one only at $\varphi<0.02$ contrary to
$\varphi<1$ as claimed in the literature.
