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This paper presents an approach to frame semantic role labeling (FSRL), a task in natural language processing that identifies semantic roles within a text following the theory of frame semantics. Unlike previous approaches which do not adequately model correlations and interactions amongst arguments, we propose arbitrary-order conditional random fields (CRFs) that are capable of modeling full interaction amongst an arbitrary number of arguments of a given predicate. To achieve tractable representation and inference, we apply canonical polyadic decomposition to the arbitrary-order factor in our proposed CRF and utilize mean-field variational inference for approximate inference. We further unfold our iterative inference procedure into a recurrent neural network that is connected to our neural encoder and scorer, enabling end-to-end training and inference. Finally, we also improve our model with several techniques such as span-based scoring and decoding. Our experiments show that our approach achieves state-of-the-art performance in FSRL.