  We present a precise solution of the polaron problem by a novel Monte Carlo
method. Basing on conventional diagrammatic expansion for the Green function of
the polaron, $G({\bf k}, \tau)$, we construct a process of generating
continuous random variables ${\bf k}$ and $\tau$, with the distribution
function exactly coinciding with $G({\bf k}, \tau)$. The polaron spectrum is
extracted from the asymptotic behavior of the Green function. We compare our
results for the polaron energy with the variational treatment of Feynman, and
for the first time present precise dispersion curve which features an ending
point at finite momentum.
