River avulsions shape vast floodplains that support populations and pose significant hazards. While previous studies emphasize climate change's role in small-to-medium avulsions, the general relationship between sediment flux, water discharge, erodibility, and large-scale avulsion occurrence in large river systems is poorly understood. Here, we use a fluvial erosion-deposition landscape evolution model to identify key controls on large-scale avulsions (i.e., displacing the river mouth >400 km) in the Lower Yellow River (LYR) over the past 100 kyr. Our model reproduces observed sediment flux magnitudes and spatiotemporal patterns of large-scale LYR avulsions. We show that erodibility and sediment deposition efficiency, through their control on magnitudes of sediment flux and deposition, primarily control large-scale LYR avulsion occurrence, while climate factors such as annual precipitation and sea-level change exert secondary influences. Large-scale LYR avulsion follows a preparatory stage, during which sediment accumulates upstream of the potential avulsion site, raising the riverbed, while headward erosion downstream lowers it, ultimately promoting the occurrence of large-scale LYR avulsion. We also evaluate the levels of fluvial erosion and sediment deposition necessary to trigger such large-scale LYR avulsions. Crossing a sediment flux threshold within the observed range is required to trigger large-scale LYR avulsions, but no significant relationship is found between sediment flux magnitude and avulsion frequency. Our findings clarify how integrated effects of erosion and sedimentation, together with changes in climate and sea level, drive large-scale LYR avulsions. More broadly, our work provides insights into the relationship between sediment flux and large-scale avulsion in river systems.