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.

翻译：参数估计作为一类经典的反问题，往往具有不适定性，因为不同的参数组合可能产生相同的输出。这种非唯一性对实现精确且唯一的辨识构成了关键障碍。本研究引入了一种新颖的参数估计框架以应对此类限制：基于联合条件扩散模型的反问题求解器（JCDI）。通过利用扩散模型的随机性，JCDI能够生成揭示潜在分布的可能解。对多个观测值的联合条件约束进一步缩小了不可辨识参数的后验分布。针对动态电力系统中的挑战性任务——综合负荷模型参数化，JCDI相比单条件模型实现了58.6%的参数估计误差降低。它还能准确复现系统在各种电气故障下的动态响应，均方根误差低于4*10^(-3)，其性能优于现有的深度强化学习和监督学习方法。鉴于其数据驱动特性，JCDI为参数估计提供了一个通用框架，同时有效缓解了跨科学领域的非唯一性挑战。