arXiv:2411.10431v2 Announce Type: replace Abstract: Parameter estimation, which represents a classical inverse problem, is often ill-posed as different parameter combinations can yield identical outputs. This non-uniqueness poses a critical barrier to accurate and unique identification. This work introduces a novel parameter estimation framework to address such limits: the Joint Conditional Diffusion Model-based Inverse Problem Solver (JCDI). By leveraging the stochasticity of diffusion models, JCDI produces possible solutions revealing underlying distributions. Joint conditioning on multiple observations further narrows the posterior distributions of non-identifiable parameters. For the challenging task in dynamic power systems: composite load model parameterization, JCDI achieves a 58.6% reduction in parameter estimation error compared to the single-condition model. It also accurately replicates system's dynamic responses under various electrical faults, with root mean square errors below 4*10^(-3), outperforming existing deep-reinforcement-learning and supervised learning approaches. Given its data-driven nature, JCDI provides a universal framework for parameter estimation while effectively mitigating the non-uniqueness challenge across scientific domains.