Title: Approximate Bijective Correspondence for isolating factors of variation. Abstract: Representational learning forms the backbone of most deep learning applications, and the value of a learned representation is intimately tied to its information content regarding different factors of variation. Finding good representations depends on the nature of supervision and the learning algorithm. We propose a novel algorithm that relies on a weak form of supervision where the data is partitioned into sets according to certain \textit{inactive} factors of variation. Our key insight is that by seeking approximate correspondence between elements of different sets, we learn strong representations that exclude the inactive factors of variation and isolate the \textit{active} factors which vary within all sets. Importantly, the information isolated is complementary to that of most other contrastive learning approaches, which isolate the inactive factors of variation. We demonstrate that the method can work in a semi-supervised scenario, and that a portion of the unsupervised data can belong to a different domain entirely. Further control over the content of the learned representations is possible by folding in data augmentation to suppress nuisance factors. We outperform competing baselines on the challenging problem of synthetic-to-real object pose transfer.