  This paper proposes a simple self-supervised approach for learning a
representation for visual correspondence from raw video. We cast correspondence
as prediction of links in a space-time graph constructed from video. In this
graph, the nodes are patches sampled from each frame, and nodes adjacent in
time can share a directed edge. We learn a representation in which pairwise
similarity defines transition probability of a random walk, so that long-range
correspondence is computed as a walk along the graph. We optimize the
representation to place high probability along paths of similarity. Targets for
learning are formed without supervision, by cycle-consistency: the objective is
to maximize the likelihood of returning to the initial node when walking along
a graph constructed from a palindrome of frames. Thus, a single path-level
constraint implicitly supervises chains of intermediate comparisons. When used
as a similarity metric without adaptation, the learned representation
outperforms the self-supervised state-of-the-art on label propagation tasks
involving objects, semantic parts, and pose. Moreover, we demonstrate that a
technique we call edge dropout, as well as self-supervised adaptation at
test-time, further improve transfer for object-centric correspondence.
