To exploit the sparsity of the considered system, the diffusion proportionate-type least mean square (PtLMS) algorithms assign different gains to each tap in the convergence stage while the diffusion sparsity-constrained LMS (ScLMS) algorithms pull the components towards zeros in the steady-state stage. In this paper, by minimizing a differentiable cost function that utilizes the Riemannian distance between the updated and previous weight vectors as well as the L0 norm of the weighted updated weight vector, we propose a diffusion L0-norm constraint improved proportionate LMS (L0-IPLMS) algorithm, which combines the benefits of the diffusion PtLMS and diffusion ScLMS algorithms and performs the best performance among them. Simulations in a system identification context confirm the improvement of the proposed algorithm.