We show that the standard concepts of nonlinear response to electromagnetic fields break down in two-dimensional Dirac systems, like graphene, in the quantum regime close to the Dirac point. We present a compelling many-body theory for nonlinear transport focusing on disorder scattering as a benchmark example. We show that, although the diamagnetic two-photon vertex is absent at the non-interacting level, disorder effects give rise to a self-generation of such two-photon vertex surviving even in the clean limit. We predict that the two-photon vertex self-generation is present only in two dimensions. The impact of such a striking scenario on the nonlinear quantum transport is discussed, predicting a huge enhancement of third-order dc conductivity comparing to the common models.