We show that a scale-invariant approximation to the next-to-leading-order BFKL kernel, constructed via transverse momentum diagrams, has a simple conformally invariant representation in impact parameter space, i.e. [GRAPHICS] That a conformally invariant representation exists is shown first by relating the kernel directly to Feynman diagrams contributing to two-photon diffractive dissociation. (C) 1997 Elsevier Science B.V.