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In magnetic resonance imaging (MRI), bias fields are difficult to correct since they are inherently unknown. They cause intra-volume intensity inhomogeneities which limit the performance of subsequent automatic medical imaging tasks, \eg, tissue-based segmentation. Since the ground truth is unavailable, training a supervised machine learning solution requires approximating the bias fields, which limits the resulting method. We introduce implicit training which sidesteps the inherent lack of data and allows the training of machine learning solutions without ground truth. We describe how training a model implicitly for bias field correction allows using non-medical data for training, achieving a highly generalized model. The implicit approach was compared to a more traditional training based on medical data. Both models were compared to an optimized N4ITK method, with evaluations on six datasets. The implicitly trained model improved the homogeneity of all encountered medical data, and it generalized better for a range of anatomies, than the model trained traditionally. The model achieves a significant speed-up over an optimized N4ITK method—by a factor of 100, and after training, it also requires no parameters to tune. For tasks such as bias field correction - where ground truth is generally not available, but the characteristics of the corruption are known - implicit training promises to be a fruitful alternative for highly generalized solutions.