Induced photon correlations are directly demonstrated by exploring two coupled nonlinear processes in an integrated device. Using orthogonally polarized modes within an integrated microring cavity, phase matching of two different nonlinear four-wave mixing processes is achieved simultaneously, wherein both processes share one target frequency mode, while their other frequency modes differ. The overlap of these modes leads to the coupling of both nonlinear processes, producing photon correlations. The nature of this process is confirmed by means of time- and power-dependent photon correlation measurements. These findings are relevant to the fundamental understanding of spontaneous parametric effects as well as single-photon-induced processes, and their effect on optical quantum state generation and control. © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim