We report the picosecond spin current generation from the interface between a heavy metal and a vicinal antiferromagnet insulator Cr_{2}O_{3} by laser pulses at room temperature and zero magnetic field. It is converted into a detectable terahertz emission in the heavy metal via the inverse spin Hall effect. The vicinal interfaces are apparently the source of the picosecond spin current, as evidenced by the proportional terahertz signals to the vicinal angle. We attribute the origin of the spin current to the transient magnetic moment generated by an interfacial nonlinear magnetic-dipole difference-frequency generation. We propose a model based on the in-plane inversion symmetry breaking to quantitatively explain the terahertz intensity with respect to the angles of the laser polarization and the film azimuth. Our work opens new opportunities in antiferromagnetic and ultrafast spintronics by considering symmetry breaking.