This paper proposes diagnostic and evolutionary models for the spatial equilibrium allocation of transboundary water resources, aiming to improve the match between riparian countries’ water allocations, and their natural, social and economic factors. The paper develops a two-stage diagnostic model to diagnose the spatial equilibrium for allocation schemes of transboundary water resources. The first stage is the matching diagnosis, and the second stage is the suitability diagnosis, which diagnoses the correctness of the size relationship or size degree of the allocated water volumes in the pair of riparian countries. For allocation schemes that have not passed the diagnosis, this study improves the scheme based on an evolutionary model by establishing rules for adjusting the amount of water. The model is applied to the Lancang–Mekong River basin. The results show that the spatial equilibrium allocation scheme in the Lancang–Mekong River Basin has improved the overall equilibrium of the water quantity allocation scheme of the river basin compared to the existing one, making it more acceptable to riparian countries. Policy recommendations are made on aspects such as improving information exchange platforms and establishing benefit compensation mechanisms. This paper provides a new quantitative analysis method for the allocation of transboundary water resources.