  Point cloud upsampling is to densify a sparse point set acquired from 3D
sensors, providing a denser representation for the underlying surface. Existing
methods divide the input points into small patches and upsample each patch
separately, however, ignoring the global spatial consistency between patches.
In this paper, we present a novel method PC$^2$-PU, which explores
patch-to-patch and point-to-point correlations for more effective and robust
point cloud upsampling. Specifically, our network has two appealing designs:
(i) We take adjacent patches as supplementary inputs to compensate the loss
structure information within a single patch and introduce a Patch Correlation
Module to capture the difference and similarity between patches. (ii) After
augmenting each patch's geometry, we further introduce a Point Correlation
Module to reveal the relationship of points inside each patch to maintain the
local spatial consistency. Extensive experiments on both synthetic and real
scanned datasets demonstrate that our method surpasses previous upsampling
methods, particularly with the noisy inputs. The code and data are at
\url{https://github.com/chenlongwhu/PC2-PU.git}.
