We demonstrate mid-infrared (MIR) frequency combs at 10 GHz repetition rate via intra-pulse difference-frequency generation (DFG) in quasi-phase-matched nonlinear media. Few-cycle pump pulses ( ≲ 15 f s , 100 pJ) from a near-infrared electro-optic frequency comb are provided via nonlinear soliton-like compression in photonic-chip silicon-nitride waveguides. Subsequent intra-pulse DFG in periodically poled lithium niobate waveguides yields MIR frequency combs in the 3.1–4.8 µm region, while orientation-patterned gallium phosphide provides coverage across 7–11 µm. Cascaded second-order nonlinearities simultaneously provide access to the carrier–envelope-offset frequency of the pump source via in-line f - 2 f nonlinear interferometry. The high-repetition rate MIR frequency combs introduced here can be used for condensed phase spectroscopy and applications such as laser heterodyne radiometry.