Causal Diffusion Models for Counterfactual Outcome Distributions in Longitudinal Data

Longitudinal treatment decisions from multivariate time-series data require predicting potential outcomes under future treatment sequences in the presence of time-varying confounding, heterogeneous patient dynamics, and limited domain-specific data. Existing longitudinal causal estimators typically address this problem by training a new model for each cohort or simulator. We introduce Causal Longitudinal Prior-Fitted Networks (CausalLongPFN), a prior-fitted network for time-series causal inference in longitudinal treatment-response data and zero-shot in-context counterfactual outcome prediction. The model is pretrained entirely on synthetic episodes sampled from a broad prior over temporal structural causal models, exposing it to treatment-confounder feedback, latent heterogeneity, nonlinear state evolution, delayed effects, and cumulative treatment responses. At test time, CausalLongPFN remains frozen and is used zero-shot: it conditions on support trajectories, a query history, and a planned future treatment sequence, and returns a predictive distribution over future outcomes without gradient updates or propensity-model fitting. Multi-step predictions are obtained by recursively applying the one-step predictor under the specified treatment sequence. We evaluate the model on branchable cancer, HIV, and warfarin benchmarks with ground-truth counterfactual labels, and on factual-only rolling-origin prediction in MIMIC-III ICU trajectories. CausalLongPFN is competitive with domain-trained longitudinal baselines on counterfactual benchmarks and performs strongly on factual MIMIC-III prediction, suggesting that broad synthetic causal pretraining can provide a frozen, amortized alternative for zero-shot longitudinal treatment-response prediction when repeated domain-specific training is costly or impractical.

Estimating counterfactual outcomes over time from longitudinal observational data is central to clinical decision support. Existing methods rely on domain confusion -- adversarial training that renders representations invariant to treatment assignment -- yet this invariance creates a mutual information conflict: it suppresses treatment-correlated covariate signals necessary for accurate outcome prediction. We formalise this tension via a Jensen-Shannon divergence bound on counterfactual prediction error and develop two complementary models. CSSD (Causal State-Space model with Direct decoder) adapts selective State Space Models with a parallel multi-step decoder that eliminates accumulated rollout error by producing all prediction horizons simultaneously in a single forward pass. CSSPD (Causal State-Space model with Predictive regularisation and Direct decoder) augments CSSD with Contrastive Predictive Coding and Local Information Maximisation to reinforce temporal predictability in the balancing representation and recover local covariate information destroyed by domain confusion. On MIMIC-III, CSSPD achieves lower counterfactual RMSE than the Causal Transformer at every horizon tau >= 2 at O(T) encoder cost, with gains from 0.02 (2-step) to 0.07 (6-step). On Cancer Simulation across confounding strengths gamma in {0,1,2,3,4}, CSSPD outperforms CT at gamma <= 3 (margins 25.9%--37.0%), and CSSD achieves the lowest overall average RMSE (12.7% reduction over CT), confirming the MI conflict analysis. To our knowledge, this is the first work to formalise the balancing-prediction MI conflict and propose a structured resolution through complementary predictive and information-theoretic training objectives.

Counterfactual inference approaches for sequential decision-making typically assume deterministic causal models, where all randomness stems from latent variables. However, Markov Decision Processes (MDPs) are inherently stochastic. We address this by formalising counterfactual policy optimisation under probabilistic nondeterministic causal models, which properly separates latent confounding from irreducible stochasticity, and here propose a first practical optimisation problem for identifying robust counterfactual policies under a sensitivity analysis framework. We validate our approach on a sepsis treatment simulator, where diabetes status acts as a hidden global confounder.