We introduce a Lennard-Jones layer (LJL) to equalize the density across the distribution of 2D and 3D point clouds by systematically rearranging points without destroying their overall structure (distribution normalization). LJL simulates a dissipative process of repulsive and weakly attractive interactions between individual points by solely considering the nearest neighbor of each point at a given moment in time. This pushes the particles into a potential valley, reaching a well-defined stable configuration that approximates an equidistant sampling after the stabilization process. We apply LJLs to redistribute randomly generated point clouds into a randomized uniform distribution over the 2D Euclidean plane and 3D mesh surfaces. Moreover, LJLs are embedded in point cloud generative network architectures by adding them at later stages of the inference process. The improvements coming with LJLs for generating 3D point clouds are evaluated qualitatively and quantitatively. Finally, we apply LJLs to improve the point distribution of a score-based 3D point cloud denoising network. In general, we demonstrate that LJLs are effective for distribution normalization which can be applied at negligible cost without retraining the given neural networks.