Quantitative models of cell migration are central to biomechanics, tissue organisation, and disease progression. Agent--based models with persistent stochastic movement rules are widely used to describe migrating cells, yet their reliance on discrete sampling complicates parameter inference, uncertainty quantification, and integration with data--driven workflows. We present a differentiable surrogate framework for cell migration models based on conditional density learning. Mixture Density Networks are trained to approximate the full transition density of cell velocities conditioned on observable state variables, learning effective migration laws directly from trajectory data. This preserves essential temporal structure such as persistence and turning behaviour, while providing a smooth likelihood suitable for gradient--based inverse analysis. We demonstrate that the approach enables simulation--free calibration of mechanistic migration parameters, recovering persistence and directional bias from synthetic and experimental cell trajectories with quantified uncertainty. Validation on real cell migration data shows that the learned surrogates accurately reproduce velocity distributions, autocorrelation structure, and turning statistics, while remaining robust to measurement noise and missing observations. By combining experimental trajectories with differentiable surrogate models, this framework provides a practical route towards data--assimilated, uncertainty--aware calibration of agent--based cell migration models, facilitating their integration into multiscale biomechanical and mechanobiological modelling pipelines.