We review a dispersive calculation of the D-term form factor, using unsubtracted $t$-channel dispersion relations for the deeply virtual Compton scattering amplitudes. The $t$-channel unitarity relation is saturated with the contribution of two-pion intermediate states, using the two-pion generalized distributions amplitude for the $\gamma^*\gamma\rightarrow \pi \pi$ subprocess and reconstructing the $\pi\pi\rightarrow N\bar{N}$ subprocess from available information on pion-nucleon partial-wave helicity amplitudes. The dispersion-relation results are discussed in comparison with available model predictions and phenomenological extractions.