Self-phase modulation (SPM) broadening of laser spectra was studied in a transmission mode in natural and synthetic diamonds at variable laser wavelengths (515 and 1030 nm), pulse energies and widths (0.3 - 12 ps, positively chirped pulses), providing their filamentary propagation. Besides the monotonous SPM broadening of the laser spectra versus pulse energy, more pronounced for the (sub)picosecond pulsewiths and more doped natural diamond, periodical low-frequency modulation was observed in the spectra at the shorter laser pulsewidths, indicating dynamic Bragg filtering of the supercontinuum due to ultrafast plasma and nanoplasmonic effects. Damping of broadening and ultramodulation for the longer picosecond pulsewidths was related to thermalized electron-hole plasma regime established for the laser pulsewidths longer, than 2 ps. Unexpectedly, at higher pulse energies and corresponding longer microfilaments, the number of spectral modulation features increases, indicating dynamic variation of the periods in the longitudinal plasma Bragg gratings along the filaments due to prompt secondary laser-plasmon interactions.