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Generalization beyond the training distribution is a core challenge in machine learning. The common practice of mixing and shuffling examples when training neural networks may not be optimal in this regard. We show that partitioning the data into well-chosen, non-i.i.d. subsets treated as multiple training environments can guide the learning of models with better out-of-distribution generalization. We describe a training procedure to capture the patterns that are stable across environments while discarding spurious ones. The method makes a step beyond correlation-based learning: the choice of the partitioning allows injecting information about the task that cannot be otherwise recovered from the joint distribution of the training data. We demonstrate multiple use cases with the task of visual question answering, which is notorious for dataset biases. We obtain significant improvements on VQA-CP, using environments built from prior knowledge, existing meta data, or unsupervised clustering. We also get improvements on GQA using annotations of "equivalent questions", and on multi-dataset training (VQA v2 / Visual Genome) by treating them as distinct environments.