We consider a multiplicatively renormalizable higher-derivative scalar theory which is used as an effective theory for quantum gravity at large distances (infrared phase of quantum gravity). The asymptotic regimes (in particular, the asymptotically free infrared regime) for the coupling constants---specifically the Newtonian and the cosmological constant---are obtained. The running of the Newton and cosmological constants in the infrared asymptotically free regime may be relevant for solving the cosmological constant problem and for estimating the leading-log corrections to the static gravitational potential.