Block ciphers are protected against side-channel attacks by masking. On one hand, when the leakage model is unknown, second-order correlation attacks are typically used. On the other hand, when the leakage model can be profiled, template attacks are prescribed. But what if the profiled model does not exactly match that of the attacked device? One solution consists in regressing on-the-fly the scaling parameters from the model. In this paper, we leverage an Expectation-Maximization (EM) algorithm to implement such an attack. The resulting unprofiled EM attack, termed U-EM, is shown to be both efficient (in terms of number of traces) and effective (computationally speaking). Based on synthetic and real traces, we introduce variants of our U-EM attack to optimize its performance, depending on trade-offs between model complexity and epistemic noise. We show that the approach is flexible, in that it can easily be adapted to refinements such as different points of interest and number of parameters in the leakage model.