Lattice vibrations have been investigated in TiB2, ZrB2 and HfB2 by temperature-dependent extended X-ray absorption fine structure (EXAFS) experiments. Data clearly show that the EXAFS oscillations are characterized by an anomalous behavior of the Debye-Waller factor of the transition-metal-boron pair, which is suggested to be associated with a superposition of an optical mode corresponding to phonon vibrations induced by the B sublattice and an acoustic mode corresponding to the transition-metal (TM) sublattice. Data can be interpreted as a decoupling of the metal and boron vibrations observed in these transition-metal diborides (TMB2), a mechanism that may be responsible for the significant reduction of the superconducting transition temperature observed in these systems with respect to the parent MgB2 compound. The vibrational behavior of TM-TM bonds has also been investigated to study the occurrence of anisotropy and anomalies in the lattice vibrational behavior of TM-TM bonds.