Latent Causal Diffusion Models for Counterfactual Generation of Physical Fields Under Non-Ideal Observations

Generative modeling of complex physical systems must not only satisfy the corresponding physical properties, but also characterize how the underlying physical process evolves when physical parameters or operating conditions change. Such questions can be viewed as counterfactual problems. However, mainstream counterfactual methods primarily operate at the level of statistical data and do not explicitly represent variable couplings constrained by physical theory, making it difficult to ensure that generated results obey structural constraints and evolution laws of physical fields. To address this issue, this paper proposes a latent causal diffusion framework for counterfactual generation of physical fields under non-ideal real-world observations. For the first time, the framework unifies physical-parameter conditions and sensor-observation conditions as controllable intervention variables. By preserving the sample initial state and non-intervened factors, the model generates paired counterfactual fields with different physical parameters under different non-ideal observation conditions. We study three-dimensional electromagnetic fields and construct counterfactual simulation experiments using gprMax/FDTD and the proposed model. The results show that the model supports counterfactual generation for multiple physical parameters and reconstruction from sparse observations under different observation conditions, and achieves directionally consistent but limited downstream correction under missing-not-at-random (MNAR) observations. However, the overall paired improvement of the proposed method has a 95% confidence interval of [−0.00417,0.04261], and the gain depends on the parameter family.