Purpose Patient‐induced inhomogeneities in the static magnetic field cause distortions and blurring (off‐resonance artifacts) during acquisitions with long readouts such as in SWI. Conventional versatile correction methods based on extended Fourier models are too slow for clinical practice in computationally demanding cases such as 3D high‐resolution non‐Cartesian multi‐coil acquisitions. Theory Most reconstruction methods can be accelerated when performing off‐resonance correction by reducing the number of iterations, compressed coils, and correction components. Recent state‐of‐the‐art unrolled deep learning architectures could help but are generally not adapted to corrupted measurements as they rely on the standard Fourier operator in the data consistency term. The combination of correction models and neural networks is therefore necessary to reduce reconstruction times. Methods Hybrid pipelines using UNets were trained stack‐by‐stack over 99 SWI 3D SPARKLING 20‐fold accelerated acquisitions at 0.6 mm isotropic resolution using different off‐resonance correction methods. Target images were obtained using slow model‐based corrections based on self‐estimated field maps. The proposed strategies, tested over 11 volumes, are compared to model‐only and network‐only pipelines. Results The proposed hybrid pipelines achieved scores competing with two to three times slower baseline methods, and neural networks were observed to contribute both as pre‐conditioner and through inter‐iteration memory by allowing more degrees of freedom over the model design. Conclusion A combination of model‐based and network‐based off‐resonance correction was proposed to significantly accelerate conventional methods. Different promising synergies were observed between acceleration factors (iterations, coils, correction) and model/network that could be expanded in the future.