We study models of inflation where the inflation corresponds to a flat direction and its mass-squared is generated by gravity mediated soft supersymmetry breaking at high scale. If the inflation has non negligible couplings to other fields, its mass runs with the scale and can reach the small value required by slow roll inflation at lower scale. Slow roll inflation can therefore take place in such a regime, but the spectral index is then scale dependent. We explore the parameter space of this kind of models to find the region compatible with the present observations. ©1999 American Institute of Physics.