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This paper studies the problem of joint estimation of data and channels for orthogonal frequency-division multiplexing (OFDM) systems using variational inference. The proposed methods are used to combat imperfect channel estimation at the receiver since it can degrade system performance seriously. The proposed methods simplify the maximum a posteriori (MAP) scheme based on the theory of variational inference and formulate an optimization problem using variational free energy. The channel state information (CSI) and data are dealt with jointly and iteratively. The proposed schemes offer a variety of solutions for getting soft information when turbo equalization is implemented for coded systems. The effectiveness of the new approach is demonstrated by Monte Carlo simulations.