  The physics of Cosmic ray (CR) transport remains a key uncertainty in
assessing whether CRs can produce galaxy-scale outflows consistent with
observations. In this paper, we elucidate the physics of CR-driven galactic
winds for CR transport dominated by diffusion. A companion paper considers CR
streaming. We use analytic estimates validated by time-dependent
spherically-symmetric simulations to derive expressions for the mass-loss rate,
momentum flux, and speed of CR-driven galactic winds, suitable for
cosmological-scale or semi-analytic models of galaxy formation. For CR
diffusion coefficients $\kappa \gtrsim r_0 c_i$ where $r_0$ is the base radius
of the wind and $c_i$ is the isothermal gas sound speed, the asymptotic wind
energy flux is comparable to that supplied to CRs, and the outflow rapidly
accelerates to supersonic speeds. By contrast, for $\kappa \lesssim r_0 c_i$,
CR-driven winds accelerate more slowly and lose most of their energy to
gravity, a CR analogue of photon-tired stellar winds. Given CR diffusion
coefficients estimated using Fermi gamma-ray observations of pion decay, we
predict mass-loss rates in CR-driven galactic winds of order the star formation
rate for dwarf and disc galaxies. The dwarf galaxy mass-loss rates are small
compared to the mass-loadings needed to reconcile the stellar and dark matter
halo mass functions. For nuclear starbursts (e.g., M82, Arp 220), CR diffusion
and pion losses suppress the CR pressure in the galaxy and the strength of
CR-driven winds. We discuss the implications of our results for interpreting
observations of galactic winds and for the role of CRs in galaxy formation.
