An analytical model is presented for the evolution of wide binaries in the Galaxy. The study is pertinent to the postulated solar companion, Nemesis, which may disturb the Oort cloud and cause catastrophic comet showers to strike the earth every 26 Myr. Distant gravitational encounters are modeled by Fokker-Planck coefficients for advection and diffusion of the orbital binding energy. It is shown that encounters with passing stars cause a diffusive evolution of the binding energy and semimajor axis. Encounters with subclumps in giant molecular clouds disrupt orbits to a degree dependent on the cumulative number of stellar encounters. The time scales of the vents and the limitations of scaling laws used are discussed. Results are provided from calculations of galactic distribution of wide binaries and the evolution of wide binary orbits. 38 references.