  We introduce a class of high order accurate, semi-implicit Runge-Kutta
schemes in the general setting of evolution equations that arise as gradient
flow for a cost function, possibly with respect to an inner product that
depends on the solution, and we establish their energy stability. This class
includes as a special case high order, unconditionally stable schemes obtained
via convexity splitting. The new schemes are demonstrated on a variety of
gradient flows, including partial differential equations that are gradient flow
with respect to the Wasserstein (mass transport) distance.
