  We present an approach to learn dense, continuous 2D-3D correspondence
distributions over the surface of objects from data with no prior knowledge of
visual ambiguities like symmetry. We also present a new method for 6D pose
estimation of rigid objects using the learnt distributions to sample, score and
refine pose hypotheses. The correspondence distributions are learnt with a
contrastive loss, represented in object-specific latent spaces by an
encoder-decoder query model and a small fully connected key model. Our method
is unsupervised with respect to visual ambiguities, yet we show that the query-
and key models learn to represent accurate multi-modal surface distributions.
Our pose estimation method improves the state-of-the-art significantly on the
comprehensive BOP Challenge, trained purely on synthetic data, even compared
with methods trained on real data. The project site is at
https://surfemb.github.io/ .
