Farbod Alinezhad, Jianfei Cao, Gary J. Young, Brady Post
arXiv 14 Apr 2026 · Statistics — Machine Learning
arXiv:2604.12992 · PDF · DOI · OpenAlex · Extracted main text
Predicting counterfactual outcomes in longitudinal data, where sequential treatment decisions heavily depend on evolving patient states, is critical yet notoriously challenging due to complex time-dependent confounding and inadequate uncertainty quantification in existing methods. We introduce the Causal Diffusion Model (CDM), the first denoising diffusion probabilistic approach explicitly designed to generate full probabilistic distributions of counterfactual outcomes under sequential interventions. CDM employs a novel residual denoising architecture with relational self-attention, capturing intricate temporal dependencies and multimodal outcome trajectories without requiring explicit adjustments (e.g., inverse-probability weighting or adversarial balancing) for confounding. In rigorous evaluation on a pharmacokinetic-pharmacodynamic tumor-growth simulator widely adopted in prior work, CDM consistently outperforms state-of-the-art longitudinal causal inference methods, achieving a 15-30% relative improvement in distributional accuracy (1-Wasserstein distance) while maintaining competitive or superior point-estimate accuracy (RMSE) under high-confounding regimes. By unifying uncertainty quantification and robust counterfactual prediction in complex, sequentially confounded settings, without tailored deconfounding, CDM offers a flexible, high-impact tool for decision support in medicine, policy evaluation, and other longitudinal domains.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Melnychuk, V., Frauen, D., and Feuerriegel, S (2022) Causal Transformer for estimating counterfactual outcomes | 0.811 | 4 | 2 | 100% |
| 2 | Bica, I., Alaa, A.\ M., Jordon, J., and van der Schaar, M (2019) Estimating counterfactual treatment outcomes over time through adversarially balanced representations | 0.737 | 3 | 2 | 100% |
| 3 | Lim, B (2018) Forecasting treatment responses over time using recurrent marginal structural networks | 0.737 | 3 | 2 | 100% |
| 4 | Li, R., Shahn, Z., Li, J., Lu, M., Chakraborty, P., Sow, D., Ghalwas… (2020) G-Net: A deep learning approach to g-computation for counterfactual outcome prediction under dynamic treatment regimes | 0.644 | 2 | 2 | 100% |
| Li et al. | unmatched citation key Li et al. | 0.585 | 3 | 1 | 100% |
| Song | unmatched citation key Song | 0.511 | 2 | 1 | 100% |
| 7 | Alcaraz, J.\ M.\ L., and Strodthoff, N (2023) Diffusion-based time series imputation and forecasting with structured state space models | 0.511 | 2 | 1 | 100% |
| 8 | Kim, M., Kwon, H., Wang, C., Kwak, S., and Cho, M (2021) Relational self-attention: What’s missing in attention for video understanding | 0.511 | 2 | 1 | 100% |
| 9 | Tashiro, Y., Song, J., Song, Y., and Ermon, S (2021) CSDI: Conditional score-based diffusion models for probabilistic time series imputation | 0.511 | 2 | 1 | 100% |
| Alaa | unmatched citation key Alaa | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 94 scored citations. 3 of these could not be matched to a bibliography entry, so only the citation key is shown.