  We introduce natural deformation classes of generalized K\"ahler structures
using the Courant symmetry group. We show that these yield natural extensions
of the notions of K\"ahler class and K\"ahler cone to generalized K\"ahler
geometry. Lastly we show that the generalized K\"ahler-Ricci flow preserves
this generalized K\"ahler cone, and the underlying real Poisson tensor.
