We present a multiway fusion algorithm capable of directly processing uncertain pairwise affinities. In contrast to existing works that require initial pairwise associations, our MIXER algorithm improves accuracy by leveraging the additional information provided by pairwise affinities. Our main contribution is a multiway fusion formulation that is particularly suited to processing non-binary affinities and a novel continuous relaxation whose solutions are guaranteed to be binary, thus avoiding the typical, but potentially problematic, solution binarization steps that may cause infeasibility. A crucial insight of our formulation is that it allows for three modes of association, ranging from non-match, undecided, and match. Exploiting this insight allows fusion to be delayed for some data pairs until more information is available, which is an effective feature for fusion of data with multiple attributes/information sources. We evaluate MIXER on typical synthetic data and benchmark datasets and show increased accuracy against the state of the art in multiway matching, especially in noisy regimes with low observation redundancy. Additionally, we collect RGB data of cars in a parking lot to demonstrate MIXER's ability to fuse data having multiple attributes (color, visual appearance, and bounding box). On this challenging dataset, MIXER achieves 74% F1 accuracy and is 49x faster than the next best algorithm, which has 42% accuracy. Open source code is available at https://github.com/mit-acl/mixer.

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