  Learning signed distance functions (SDFs) from 3D point clouds is an
important task in 3D computer vision. However, without ground truth signed
distances, point normals or clean point clouds, current methods still struggle
from learning SDFs from noisy point clouds. To overcome this challenge, we
propose to learn SDFs via a noise to noise mapping, which does not require any
clean point cloud or ground truth supervision for training. Our novelty lies in
the noise to noise mapping which can infer a highly accurate SDF of a single
object or scene from its multiple or even single noisy point cloud
observations. Our novel learning manner is supported by modern Lidar systems
which capture multiple noisy observations per second. We achieve this by a
novel loss which enables statistical reasoning on point clouds and maintains
geometric consistency although point clouds are irregular, unordered and have
no point correspondence among noisy observations. Our evaluation under the
widely used benchmarks demonstrates our superiority over the state-of-the-art
methods in surface reconstruction, point cloud denoising and upsampling. Our
code, data, and pre-trained models are available at
https://github.com/mabaorui/Noise2NoiseMapping/
