Blind Source Separation (BSS) has gained a large interest in many fields, including hyperspectral unmixing which is broadly used in remote sensing and astrophysics. BSS being an ill-posed problem, many strategies have been proposed to solve it, ranging from model-based to deep-learning ones. While modelbased algorithms are in general interpretable, in contrast with neural networks, these algorithms often require a large number of iterations and obtain worse unmixing results that their deeplearning counterparts. To try to obtain the best of both worlds, in this work we unroll the multiplicative updates algorithm, leading to two new algorithms. The first one, NALMU, learns some parameters which are fixed once the training is over. The second one, ALMU, enables the parameters of the unrolled algorithm to be predicted by small neural networks, making the whole algorithm adaptative to the specific datasets considered in the test phase. We conduct experiments on two astrophysic datasets, and show that our approach enables to largely outperform the other unmixing unrolled algorithms, while largely reducing the number of iterations compared to the original multiplicative updates algorithm.