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Ultra-fine entity typing (UFET) aims to predict a wide range of type phrases that correctly describe the categories of a given entity mention in a sentence. Most recent works infer each entity type independently, ignoring the correlations between types, e.g., when an entity is inferred as a president, it should also be a politician and a leader. To this end, we use an undirected graphical model called pairwise conditional random field (PCRF) to formulate the UFET problem, in which the type variables are not only unarily influenced by the input but also pairwisely relate to all the other type variables. We use various modern backbones for entity typing to compute unary potentials, and derive pairwise potentials from type phrase representations that both capture prior semantic information and facilitate accelerated inference. We use mean-field variational inference for efficient type inference on very large type sets and unfold it as a neural network module to enable end-to-end training. Experiments on UFET show that the Neural-PCRF consistently outperforms its backbones with little cost and results in a competitive performance against cross-encoder based SOTA while being thousands of times faster. We also find Neural- PCRF effective on a widely used fine-grained entity typing dataset with a smaller type set. We pack Neural-PCRF as a network module that can be plugged onto multi-label type classifiers with ease and release it in https://github.com/modelscope/adaseq/tree/master/examples/NPCRF.