We present an implementation of dispersion-scan based on self-diffraction (SD d-scan) and apply it to the measurement of over octave-spanning sub-4-fs pulses. The results are compared with second-harmonic generation (SHG) d-scan. The efficiency of the SD process is derived theoretically and compared with the spectral response retrieved by the d-scan algorithm. The new SD d-scan has a robust inline setup and enables measuring pulses with over-octave spectra, single-cycle durations, and wavelength ranges beyond those of SHG crystals, such as the ultraviolet and the deep-ultraviolet.