High-resolution, high signal-to-noise ratio line profiles are presented for the 5780 and 5797 A diffuse interstellar bands toward six stars in the Rho Oph dark cloud. Target stars were chosen to exhibit a wide range of interstellar grain properties, as measured by grain polarization and far-UV extinction. The extreme case of the heavily reddened star HD 147889 is included; this star has one of the highest known lambdamax values, indicative of unusually large grains. Despite the differences in the grain properties, the line profiles and central wavelengths for the 5780 A band were found to be essentially identical for all lines of sight. This finding is in contradiction to the results of the embedded cavity grain model for diffuse bands, which predicts changes in both profile and central wavelength with grain size and impurity concentration. Results therefore support a molecular origin for the diffuse bands
