Modes of propagation are generally defined as the eigensolutions of the wave equation in a given system. When propagation occurs through complicated or highly scattering media, however, modes are better identified as the best orthogonal communication channels to send information between sets of input and output apertures. Here, we demonstrate that we can find optimum bi-directional orthogonal communication channels through arbitrary and scattering optical systems using photonic processors. The processors, made from meshes of tunable Mach-Zehnder interferometers in silicon photonics, configure themselves based on simple power maximization or minimization algorithms, without external calculations or calibration or any prior knowledge of the optical system. The resulting communication mode channels correspond to a singular-value decomposition, performed by the photonic processors, of the entire complex optics. Cross-talk below -30dB is observed between channels even in the presence of distorting masks or partial obstructions; in such cases, the beams bear little resemblance to conventional mode families, but show orthogonality nonetheless.