Predicting geohazard runout is critical for protecting lives, infrastructure and ecosystems. Rapid mass flows, including landslides and avalanches, cause several thousand deaths across a wide range of environments, often travelling many kilometres from their source. The wide range of source conditions and material properties governing these flows makes their runout difficult to anticipate, particularly for downstream communities that may be suddenly exposed to severe impacts. Accurately predicting runout at scale requires models that are both physically realistic and computationally efficient, yet existing approaches face a fundamental speed-realism trade-off. Here we train a machine learning model to predict geohazard runout across representative real world terrains. The model predicts both flow extent and deposit thickness with high accuracy and 100 to 10,000 times faster computation than numerical solvers. It is trained on over 100,000 numerical simulations across over 10,000 real world digital elevation model chips and reproduces key physical behaviours, including avulsion and deposition patterns, while generalizing across different flow types, sizes and landscapes. Our results demonstrate that neural emulation enables rapid, spatially resolved runout prediction across diverse real world terrains, opening new opportunities for disaster risk reduction and impact-based forecasting. These results highlight neural emulation as a promising pathway for extending physically realistic geohazard modelling to spatial and temporal scales relevant for large scale early warning systems.