We have measured the vibrational energy relaxation of azulene in the S-2 state in ethane, carbon dioxide, and xenon over a wide density region by the time-resolved fluorescence spectroscopy. The reduced density of the solvent (the density divided by the critical density) has been changed from the gaslike one (lower than 0.05) to the liquidlike one (2.8 for ethane, 2.7 for carbon dioxide, and 2.0 for xenon). The density dependence of the relaxation rate is compared with that of azulene in the S-0 state [D. Schwarzer, J. Troe, M. Votsmeier, and M. Zerezke, J. Chem. Phys. 105, 3121 (1996)]. Although the absolute rate largely depends on the electronic state, the density dependence of the relaxation rates is roughly the same for both electronic states, which can be considered as a side-proof of the isolated binary collision model. Possible origins for the validity of the isolated binary collision model are discussed.