Spatial modulation orthogonal frequency division multiplexing with subcarrier index modulation (ISM-OFDM) is a novel OFDM technique that conveys additional information bits by active antenna indices and grouped subcarrier indices. However, it takes a huge amount of resources to acquire the channel state information (CSI) at the receiver. In this paper, we propose two differential spatial frequency modulation with orthogonal frequency division multiplexing (DSFM-OFDM) systems, termed DSFM-OFDM-single (DSFM-OFDM-S) and DSFM-OFDM- multiple (DSFM-OFDM-M) over space-time-frequency, which completely avoid the need for CSI at the transmitter and receiver. In DSFM-OFDM, the transmitted symbols are modulated through ordinary signal modulation. And then part of some additional information bits are transmitted by selecting a permutation of the active antennas, whereas another part of it are employed to determine the subcarrier index matrices. Simulation results show that at low spectral efficiency, the performance of the proposed two schemes are better than differential spatial modulation (DSM) with the high SNR. Besides, the performance degradation of DSFM-OFDM-M and DSFM- OFDM-S over ISM-OFDM can be less than 6dB. And that the loss decreases as the number of receive antennas decreases.