  We present a method to efficiently compute Wasserstein gradient flows. Our
approach is based on a generalization of the back-and-forth method (BFM)
introduced by Jacobs and L\'eger to solve optimal transport problems. We evolve
the gradient flow by solving the dual problem to the JKO scheme. In general,
the dual problem is much better behaved than the primal problem. This allows us
to efficiently run large-scale simulations for a large class of internal
energies including singular and non-convex energies.
