Although diamond photonics has driven considerable interest and useful applications, as shown in frequency generation devices and single photon emitters, fundamental studies on the third-order optical nonlinearities of diamond are still scarce, stalling the development of an integrated platform for nonlinear and quantum optics. The purpose of this paper is to contribute to those studies by measuring the spectra of two-photon absorption coefficient (β) and the nonlinear index of refraction (n2) of diamond using femtosecond laser pulses, in a wide spectral range. These measurements show the magnitude of β increasing from 0.07 to 0.23 cm/GW, as it approaches the bandgap energy, in the region from 3.18 to 4.77 eV (390-260 nm), whereas the n2 varies from zero to 1.7 × 10-19 m2/W in the full measured range, from 0.83-4.77 eV (1500-260 nm). The experimental results are compared with theoretical models for nonlinear absorption and refraction in indirect gap semiconductors, indicating the two-photon absorption as the dominant effect in the dispersion of the third-order nonlinear susceptibility. These data, together with optical Kerr gate measurements, also provided here, are of foremost relevance to the understanding of ultrafast optical processes in diamond and its nonlinear optical properties.