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This paper investigates multi-user detection (MUD) as well as virtual single-user detection (VSUD) for denoising-based physical network coding in two-way relay channels. In MUD, the two source messages are detected separately and then mapped into a relaying message. In VSUD, the relaying message is obtained directly by detecting the received signal. Maximum likelihood (ML) algorithm and linear algorithms are considered for both single-antenna case and multi-antenna case with and without transmit power and phase control. Suboptimal detection algorithms with lower complexity are also proposed for VSUD. Simulation results show that ML VSUD can achieve better BER performance than ML MUD. The proposed detection algorithms can achieve similar BER performance to ML VSUD .