# Causal Diffusion Models for Counterfactual Outcome Distributions in Longitudinal Data

arXiv: https://arxiv.org/abs/2604.12992 · HTML: https://mlsanity.com/paper/2604.12992/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2307.00754/) (2023)
- [Counterfactual Generative Models for Time-Varying Treatments](https://mlsanity.com/paper/2305.15742/) (2023)
- [Relational Self-Attention: What's Missing in Attention for Video Understanding](https://mlsanity.com/paper/2111.01673/) (2021)
- [G-Net: A Deep Learning Approach to G-computation for Counterfactual Outcome Prediction Under Dynamic Treatment Regimes](https://mlsanity.com/paper/2003.10551/) (2020)
- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [G-Transformer: Counterfactual Outcome Prediction under Dynamic and Time-varying Treatment Regimes](https://mlsanity.com/paper/2406.05504/) (2024)
- [Causal Time Series Generation via Diffusion Models](https://mlsanity.com/paper/2509.20846/) (2025)
- [Uncertainty-Aware Optimal Treatment Selection for Clinical Time Series](https://mlsanity.com/paper/2410.08816/) (2024)
- [TERRA: A Transformer-Enabled Recursive R-learner for Longitudinal Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2510.22407/) (2025)
- [Decision making and uncertainty quantification for individualized treatments](https://mlsanity.com/paper/1709.07498/) (2017)

## Built on by (most cited first, 1 of 1)

- [Admissible Diffusion for Multimodal Interventional Trajectories](https://mlsanity.com/paper/2609.34433/) (2026)

## Abstract (arXiv)

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.