We study experimentally nonlinear optical processes in which Stokes and anti-Stokes fields build up under strong, resonant, counterpropagating pump laser excitation in atomic sodium vapor. We find that, at some pump frequency, two off-axis anti-Stokes emissions propagating along reflection-symmetric directions are strongly temporally correlated, with a correlation time of $0.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ and a correlation range of
1mrad. It is shown by the numerical analysis based on six-wave mixing process involving pump, Stokes, and anti-Stokes waves in the forward and the backward directions that such correlated anti-Stokes emissions are possible when the medium is opaque for the Stokes field and transparent for the anti-Stokes field. Possibilities of quantum correlation for entangled photon generation using this system are discussed.