  Neural implicit surfaces can be used to recover accurate 3D geometry from
imperfect point clouds. In this work, we show that state-of-the-art techniques
work by minimizing an approximation of a one-sided Chamfer distance. This shape
metric is not symmetric, as it only ensures that the point cloud is near the
surface but not vice versa. As a consequence, existing methods can produce
inaccurate reconstructions with spurious surfaces. Although one approach
against spurious surfaces has been widely used in the literature, we
theoretically and experimentally show that it is equivalent to regularizing the
surface area, resulting in over-smoothing. As a more appealing alternative, we
propose DiffCD, a novel loss function corresponding to the symmetric Chamfer
distance. In contrast to previous work, DiffCD also assures that the surface is
near the point cloud, which eliminates spurious surfaces without the need for
additional regularization. We experimentally show that DiffCD reliably recovers
a high degree of shape detail, substantially outperforming existing work across
varying surface complexity and noise levels. Project code is available at
https://github.com/linusnie/diffcd.
