Predictive simulations hold the potential to greatly expedite advances in understanding healthy and pathological movement. We developed a computationally efficient framework to predict human movement based on optimization of a performance criterion. The framework generates three-dimensional muscle-driven simulations, without relying on experimental data, in about 36 minutes on a standard laptop—more than 20 times faster than existing simulations—by using direct collocation, implicit differential equations, and algorithmic differentiation. The simulations produce physiologically realistic gaits with varied gait speed, and changes in gait caused by muscle strength deficits or prosthesis use. We extended this framework to generate simulations that are robust to uncertainty (e.g., sensorimotor noise) to further increase the realism of our simulations. We expect these predictions to enable optimal design of treatments aiming to restore gait function.