This paper describes a technique that generates speech acoustics from articulator movements. Our motivation is to help people who can no longer speak following laryngectomy, a procedure that is carried out tens of thousands of times per year in the Western world. Our method for sensing articulator movement, permanent magnetic articulography, relies on small, unobtrusive magnets attached to the lips and tongue. Changes in magnetic field caused by magnet movements are sensed and form the input to a process that is trained to estimate speech acoustics. In the experiments reported here this “Direct Synthesis” technique is developed for normal speakers, with glued-on magnets, allowing us to train with parallel sensor and acoustic data. We describe three machine learning techniques for this task, based on Gaussian mixture models, deep neural networks, and recurrent neural networks (RNNs). We evaluate our techniques with objective acoustic distortion measures and subjective listening tests over spoken sentences read from novels (the CMU Arctic corpus). Our results show that the best performing technique is a bidirectional RNN (BiRNN), which employs both past and future contexts to predict the acoustics from the sensor data. BiRNNs are not suitable for synthesis in real time but fixed-lag RNNs give similar results and, because they only look a little way into the future, overcome this problem. Listening tests show that the speech produced by this method has a natural quality that preserves the identity of the speaker. Furthermore, we obtain up to 92% intelligibility on the challenging CMU Arctic material. To our knowledge, these are the best results obtained for a silent-speech system without a restricted vocabulary and with an unobtrusive device that delivers audio in close to real time. This work promises to lead to a technology that truly will give people whose larynx has been removed their voices back.