We develop a general approach to the evolution equations fot higher-twist parton distributions. A complete set of two-particle renormalization group kernels is derived that serve as building blocks in arbitrary QCD evolution equations to twist-four accuracy. It is shown that the $2\to 2$ evolution kernels that involve ``non-partonic'' components of field operators, and, most remarkably, also $2\to3$ splitting kernels do not require independent calculation and can be restored from the known leading-twist results using conformal symmetry and Lorentz transformations. The kernels are presented for the renormalization of light-ray operators built of chiral fields in a particular basis such that the conformal symmetry is manifest. The results can easily be recast in momentum space, in the form of evolution equations for generalized parton distributions.