  Generating dense point clouds from sparse raw data benefits downstream 3D
understanding tasks, but existing models are limited to a fixed upsampling
ratio or to a short range of integer values. In this paper, we present
APU-SMOG, a Transformer-based model for Arbitrary Point cloud Upsampling (APU).
The sparse input is firstly mapped to a Spherical Mixture of Gaussians (SMOG)
distribution, from which an arbitrary number of points can be sampled. Then,
these samples are fed as queries to the Transformer decoder, which maps them
back to the target surface. Extensive qualitative and quantitative evaluations
show that APU-SMOG outperforms state-of-the-art fixed-ratio methods, while
effectively enabling upsampling with any scaling factor, including non-integer
values, with a single trained model. The code is available at
https://github.com/apusmog/apusmog/
