Optimization plays a crucial role in a vast range of problems in science, engineering, and data analytics including the training of machine-learning models and performing statistical inference. Algorithm unrolling accelerates the iterative optimization process by learning efficient iterative updates. We propose a method that improves alternating optimization for nonnegative matrix factorization (NMF). Unlike conventional unrolling, which treats a fixed number of iterations as a parametric network, our approach learns a single update step near optimum. Furthermore, unlike most existing methods that assume a fixed sensing matrix, our model can factorize data generated through previously unseen sensing matrices. Experimental results demonstrate that a model trained on randomly generated artificial data successfully decomposes spectral data.