  We study the spatially homogeneous granular medium equation
\[\partial_t\mu=\rm{div}(\mu\nabla V)+\rm{div}(\mu(\nabla W \ast
\mu))+\Delta\mu\,,\] within a large and natural class of the confinement
potentials $V$ and interaction potentials $W$. The considered problem do not
need to assume that $\nabla V$ or $\nabla W$ are globally Lipschitz. With the
aim of providing particle approximation of solutions, we design efficient
forward-backward splitting algorithms. Sharp convergence rates in terms of the
Wasserstein distance are provided.
