Attribution methods assess the contribution of inputs to the model prediction. One way to do so is erasure: a subset of inputs is considered irrelevant if it can be removed without affecting the prediction. Though conceptually simple, erasure's objective is intractable and approximate search remains expensive with modern deep NLP models. Erasure is also susceptible to the hindsight bias: the fact that an input can be dropped does not mean that the model `knows' it can be dropped. The resulting pruning is over-aggressive and does not reflect how the model arrives at the prediction. To deal with these challenges, we introduce Differentiable Masking. DiffMask learns to mask-out subsets of the input while maintaining differentiability. The decision to include or disregard an input token is made with a simple model based on intermediate hidden layers of the analyzed model. First, this makes the approach efficient because we predict rather than search. Second, as with probing classifiers, this reveals what the network `knows' at the corresponding layers. This lets us not only plot attribution heatmaps but also analyze how decisions are formed across network layers. We use DiffMask to study BERT models on sentiment classification and question answering.