Intracortical brain-computer interfaces (iBCIs) can restore voluntary movement to people with paralysis by translating their brain activity into a control signal for an external device. Maintaining stable iBCI performance is challenging due to instabilities at the neural interface, such as shifts in electrode position in the brain or malfunctions of electrodes. Such instabilities result in a degradation of decoding performance, requiring that device use be interrupted to allow for the collection of recalibration data for the iBCI decoder. To address this challenge, an emerging class of methods leverages population-level latent manifold structure, thought to provide a more stable mapping between brain activity and behavior. In recent demonstrations, unsupervised manifold alignment achieved stable decoding performance without supervised recalibration. However, these methods do not incorporate dynamics models, which achieve higher initial iBCI decoding performance than models lacking dynamics. Thus, we developed a platform for nonlinear manifold alignment with dynamics (NoMAD) that stabilizes iBCI decoding. In NoMAD, manifold discovery is performed by latent factor analysis via dynamical systems (LFADS), a deep learning approach that uncovers dynamical structure underlying population activity. NoMAD combines LFADS with unsupervised distribution alignment to produce consistent manifold estimates that are robust to changes in the recorded neurons. We tested whether NoMAD could improve the stability of offline decoding from the motor cortex as a monkey performed an isometric wrist force task. NoMAD achieved stable, high-performance decoding of the monkey’s exerted force throughout 20 sessions spanning over three months without supervised recalibration.