  We introduce the Lennard-Jones layer (LJL) for the equalization of the
density of 2D and 3D point clouds through 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 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.
Moreover, LJLs are embedded in the generation process of point cloud networks
by adding them at later stages of the inference process. The improvements in 3D
point cloud generation utilizing LJLs 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 network.
