We propose a systematic probabilistic framework to address the phase noise (PHN) problem in OFDM. In addition to deriving the optimal data detection scheme in the presence of PHN, we introduce a series of suboptimal approaches to blindly cancel the effect of PHN without the aid of pilot symbols. Not only do these algorithms provide the means to efficiently eliminate the effect of PHN in OFDM, they also open the door to much wider applications of advanced probabilistic inference algorithms in solving communications problems.