  Strichartz estimates are derived from $\ell^2$-decoupling for phase functions
satisfying a curvature condition. Bilinear refinements without loss in the high
frequency are discussed. Estimates are established from uniform curvature
generalizing Galilean invariance or from transversality in one dimension. The
bilinear refinements are utilized to prove local well-posedness for generalized
cubic nonlinear Schr\"odinger equations.
