Latent Causal Propagation for Out-of-Distribution Single-Cell Perturbation Prediction

Predicting single-cell responses to unseen genetic or chemical perturbations requires generalization beyond the perturbations observed during training. Yet the conditions under which latent representations support such generalization remain insufficiently understood. We study this problem through latent causal propagation: perturbations intervene on a basal cell state, propagate through a shared latent structural causal model (SCM), and produce transcriptional responses through a domain-invariant conditional generation kernel. Under explicit assumptions, we establish identifiability results for perturbation-induced latent distributions and, under additional restrictions, the latent structural matrix. We further characterize the cross-domain optimality of an oracle Bayes rule conditioned on the causal latent state and bound target-domain generation error in terms of latent representation and conditional generator approximation errors. Guided by this framework, we introduce scCausalDiff, which combines a learned latent SCM with conditional diffusion generation. Experiments on genetic and chemical perturbation benchmarks under strict OOD splits demonstrate competitive predictive performance across mean-response and distributional metrics.