Time- and frequency-resolved coherent anti-Stokes Raman scattering is used to carry out systematic measurements of vibrational dephasing on I2 (v = 1-19) isolated in solid Kr, as a function of temperature, T = 7-45 K. The observed quantum beats, omega(v', v") allow an accurate reconstruction of the solvated molecular potential, which is well represented by the Morse form: omega(e) = 211.56 +/- 0.14, omega(e)chi(e) = 0.658 +/- 0.006. Near T = 7 K, the coherence decay rates gamma(v,0) become independent of temperature and show a linear v-dependence, indicative of dissipation, which must be accompanied by the simultaneous creation of at least four phonons. At higher temperatures, the T-dependence is exponential and the v-dependence is quadratic, characteristic of pure dephasing via pseudo-local phonons. A normal mode analysis suggests librations as the principle modes responsible for pure dephasing.