We propose a physics-inspired, unrolled-deep-learning framework for off-resonance correction. Our forward model includes coil sensitivities, multi-frequency bins, and non-uniform Fourier transforms hence compatible with fat/water imaging and parallel imaging acceleration. The network, which includes data-consistency terms and CNN modules serving as proximal operators, is trained end-to-end using only synthetic random field maps, coil sensitivities, and noise-like images with statistics (smoothness) mimicking natural signals. Our aim is to train the network to reverse off-resonance irrespective of the type of imaging, and hence generalizable to any anatomy and contrast without retraining. We demonstrate initial results in simulations, phantom, and in-vivo data.