Precision phenomenological studies of high-multiplicity scattering processes at collider experiments present a substantial theoretical challenge and are vitally important ingredients in experimental measurements. Machine learning technology has the potential to dramatically optimise simulations for complicated final states. We investigate the use of neural networks to approximate matrix elements, studying the case of loop-induced diphoton production through gluon fusion. We train neural network models on one-loop amplitudes from the NJet C++ library and interface them with the Sherpa Monte Carlo event generator to provide the matrix element within a realistic hadronic collider simulation. Computing some standard observables with the models and comparing to conventional techniques, we find excellent agreement in the distributions and a reduced total simulation time by a factor of thirty.