Free unfolding in neutron spectroscopy means reconstructing energy spectra from experimental data without a priori assumptions regarding their shape. Due to the ill-conditioned nature of the problem, this cannot be done analytically. Neural Networks (NN) are here applied to this task and synthetic data is used for training and testing. Results showed very consistent performance especially in the region of low and medium counts, where they fall near the Poisson statistical boundary. Comparison with other unfolding methods validated these results. Application time on the order of ms makes NN suitable for real-time analysis. This approach can be applied to any instrument of which the response function is known.