  We derive new gradient flows of divergence functions in the probability space
embedded with a class of Riemannian metrics. The Riemannian metric tensor is
built from the transported Hessian operator of an entropy function. The new
gradient flow is a generalized Fokker-Planck equation and is associated with a
stochastic differential equation that depends on the reference measure. Several
examples of Hessian transport gradient flows and the associated stochastic
differential equations are presented, including the ones for the reverse
Kullback--Leibler divergence, alpha-divergence, Hellinger distance, Pearson
divergence, and Jenson--Shannon divergence.
