We propose a data-efficient, physics-aware generative framework in function space for inverse PDE problems. Existing plug-and-play diffusion posterior samplers represent physics implicitly through joint coefficient-solution modeling, requiring substantial paired supervision. In contrast, our Decoupled Diffusion Inverse Solver (DDIS) employs a decoupled design: an unconditional diffusion learns the coefficient prior, while a neural operator explicitly models the forward PDE for guidance. This decoupling enables superior data efficiency and effective physics-informed learning, while naturally supporting Decoupled Annealing Posterior Sampling (DAPS) to avoid over-smoothing in Diffusion Posterior Sampling (DPS). Theoretically, we prove that DDIS avoids the guidance attenuation failure of joint models when training data is scarce. Empirically, DDIS achieves state-of-the-art performance under sparse observation, improving $l_2$ error by 11% and spectral error by 54% on average; when data is limited to 1%, DDIS maintains accuracy with 40% advantage in $l_2$ error compared to joint models.

翻译：我们提出了一种面向偏微分方程逆问题的函数空间数据高效、物理感知生成框架。现有即插即用扩散后验采样器通过联合系数-解建模隐式表达物理规律，需要大量配对监督数据。与之相对，我们提出的解耦扩散逆求解器采用解耦设计：无条件扩散模型学习系数先验分布，而神经算子显式建模前向偏微分方程以提供指导。这种解耦机制实现了卓越的数据效率和有效的物理信息学习，同时天然支持解耦退火后验采样以避免扩散后验采样中的过度平滑问题。理论上，我们证明当训练数据稀缺时，DDIS能够避免联合模型存在的指导衰减失效问题。实证结果表明，在稀疏观测条件下，DDIS取得了最先进的性能，平均将$l_2$误差降低11%，谱误差降低54%；当数据量限制在1%时，相较于联合模型，DDIS在$l_2$误差上仍保持40%的优势精度。