The diffusive streaming of 1.3 to 2.3-MeV per nucleon protons has been found to be predominantly toward the sun during periods between prompt solar particle events. This sunward streaming occurs for essentially all proton intensities from <0.012 to 1.2 (cm2 s sr MeV) -1 and for all solar wind velocities. The average radial component (16%¿3%) of the diffusive anisotropy of 1.4-MeV per nucleon alpha particles is very similar to that observed for protons (14%¿1%, a finding suggesting a common origin. These periods are characterized by a limited variance in the proton intensities (10-1.2¿1.1 cm-2 s-1 sr-1 MeV-1), in the proton spectra (E-3.00.8), and in the &agr;/p ratio (3%¿2%). The sunward diffusion of protons and alpha particles indicates tha a positive radial gradient is characteristic of these modestly enhanced fluxes. A steady state propagation model which includes adiabatic energy loss and a source of particles beyond 1 AU produces the average radial anisotropy and its dependence on the solar wind velocity forfor krr~4¿1020 cm2 s-1. The direction of the diffusive anisotropy is strongly dependent on the magnetic field direction, a situation indicating k⊥<kN. However, the two directions are not identical, a condition indicating nonnegligible flow perpendicular to the average field direction when averaged over a 6-hour interval.