How do we know a generated patch is correct? This is a key challenging question that automated program repair (APR) systems struggle to address given the incompleteness of available test suites. Our intuition is that we can triage correct patches by checking whether each generated patch implements code changes (i.e., behaviour) that are relevant to the bug it addresses. Such a bug is commonly specified by a failing test case. Towards predicting patch correctness in APR, we propose a novel yet simple hypothesis on how the link between the patch behaviour and failing test specifications can be drawn: similar failing test cases should require similar patches . We then propose BATS , an unsupervised learning-based approach to predict patch correctness by checking patch B ehaviour A gainst failing T est S pecification. BATS exploits deep representation learning models for code and patches: for a given failing test case, the yielded embedding is used to compute similarity metrics in the search for historical similar test cases to identify the associated applied patches, which are then used as a proxy for assessing the correctness of the APR-generated patches. Experimentally, we first validate our hypothesis by assessing whether ground-truth developer patches cluster together in the same way that their associated failing test cases are clustered. Then, after collecting a large dataset of 1,278 plausible patches (written by developers or generated by 32 APR tools), we use BATS to predict correct patches: BATS achieves AUC between 0.557 to 0.718 and recall between 0.562 and 0.854 in identifying correct patches. Our approach outperforms state-of-the-art techniques for identifying correct patches without the need for large labeled patch datasets; as is the case with machine learning-based approaches. While BATS is constrained by the availability of similar test cases, we show that it can still be complementary to existing approaches: when combined with a recent approach that relies on supervised learning, BATS improves the overall recall in detecting correct patches. We finally show that BATS is complementary to the state-of-the-art PATCH-SIM dynamic approach for identifying correct patches generated by APR tools.