We propose a structured prior for high-dimensional Bayesian inverse problems based on a disentangled deep generative model whose latent space is partitioned into auxiliary variables aligned with known and interpretable physical parameters and residual variables capturing remaining unknown variability. This yields a hierarchical prior in which interpretable coordinates carry domain-relevant uncertainty while the residual coordinates retain the flexibility of deep generative models. By linearizing the generator, we characterize the induced prior covariance and derive conditions under which the posterior exhibits approximate block-diagonal structure in the latent variables, clarifying when representation-level disentanglement translates into a separation of uncertainty in the inverse problem. We formulate the resulting latent-space inverse problem and solve it using MAP estimation and Markov chain Monte Carlo (MCMC) sampling. On elliptic PDE inverse problems, such as conductivity identification and source identification, the approach matches an oracle Gaussian process prior under correct specification and provides substantial improvement under prior misspecification, while recovering interpretable physical parameters and producing spatially calibrated uncertainty estimates.

翻译：我们提出一种基于解耦深度生成模型的结构化先验，用于高维贝叶斯逆问题。该模型的潜空间被划分为两组变量：一组是与已知且可解释的物理参数对齐的辅助变量，另一组是捕捉剩余未知变异的残差变量。由此构建的层次先验中，可解释坐标携带领域相关的先验不确定性，而残差坐标保留深度生成模型的灵活性。通过线性化生成器，我们刻画了诱导先验协方差，并推导出后验在潜变量中呈现近似块对角结构的条件，从而阐明表征层面的解耦如何转化为逆问题中不确定性的分离。我们制定了相应的潜空间逆问题，并通过最大后验估计和马尔可夫链蒙特卡洛采样求解。在椭圆型偏微分方程逆问题（如电导率识别和源识别）中，该方法在正确设定下匹配了高斯过程先验预言机，在先验误设下提供了显著改进，同时恢复了可解释的物理参数并生成空间校准的不确定性估计。