A novel method of intense terahertz (THz) radiation from a laser-driven magnetized plasma was studied by theory and simulations. In this newly suggested scheme, two counter-propagating laser pulses collide in a magnetized plasma, leaving a non-linear current which acts as a radiation antenna. The resulting power of the THz emission was found to be enhanced by more than hundreds of times compared to the single-pulse-driven Cherenkov wake scheme. The emission amplitude reaches tens of MV/m for 10 THz even with a low amplitude of the driving laser pulse such as a0 ∼ 0.05, and has a quasi-continuous feature with a monochromatic frequency spectrum. Two factors of the enhanced THz emission are discussed. One is the stronger ponderomotive force by the beat of counter-pulses than that of a single pulse. The other is the diffusion-like behavior of the electromagnetic field near cutoff. We theoretically found that when an electromagnetic radiation is driven near cut-off by a constant current, as in our case, the field exhibits a diffusion-like behavior with the field amplitude growing with time. As the growing field hits the plasma-vacuum boundary by the diffusion, it comes as an enhanced THz radiation in free space. This phenomenon was modeled by a constantly driven, complex diffusion equation, which was deduced from the slowly varying envelope model.