# Counterfactual Probabilistic Diffusion with Expert Models

arXiv: https://arxiv.org/abs/2508.13355 · HTML: https://mlsanity.com/paper/2508.13355/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 81 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [Feature-Conditioned Cascaded Video Diffusion Models for Precise Echocardiogram Synthesis](https://mlsanity.com/paper/2303.12644/) (2023)
- [Diffusion Models for Counterfactual Generation and Anomaly Detection in Brain Images](https://mlsanity.com/paper/2308.02062/) (2023)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2110.14690/) (2021)
- [DiffTAD: Temporal Action Detection with Proposal Denoising Diffusion](https://mlsanity.com/paper/2303.14863/) (2023)
- [DiffPO: A causal diffusion model for learning distributions of potential outcomes](https://mlsanity.com/paper/2410.08924/) (2024)
- [Causal effects based on distributional distances](https://mlsanity.com/paper/1806.02935/) (2018)
- [ACE-NODE: Attentive Co-Evolving Neural Ordinary Differential Equations](https://mlsanity.com/paper/2105.14953/) (2021)
- [When and How to Lift the Lockdown? Global COVID-19 Scenario Analysis and Policy Assessment using Compartmental Gaussian Processes](https://mlsanity.com/paper/2005.08837/) (2020)
- [Disentangled Counterfactual Recurrent Networks for Treatment Effect Inference over Time](https://mlsanity.com/paper/2112.03811/) (2021)

## Built on by (most cited first, 4 of 4)

- [GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes](https://mlsanity.com/paper/2509.22953/) (2025)
- [What if Tomorrow is the World Cup Final? Counterfactual Time Series Forecasting with Textual Conditions](https://mlsanity.com/paper/2605.14422/) (2026)
- [Benchmarking Counterfactual Prediction in Epidemic Time Series with Time-Varying Interventions](https://mlsanity.com/paper/2606.05692/) (2026)
- [OrthoGen: A Generative Orthogonal Learner for Time-Varying Treatments](https://mlsanity.com/paper/2610.10210/) (2026)

## Abstract (arXiv)

Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely data-driven models, which tend to falter under data scarcity. We propose a time series diffusion-based framework that incorporates guidance from imperfect expert models by extracting high-level signals to serve as structured priors for generative modeling. Our method, ODE-Diff, bridges mechanistic and data-driven approaches, enabling more reliable and interpretable causal inference. We evaluate ODE-Diff across semi-synthetic COVID-19 simulations, synthetic pharmacological dynamics, and real-world case studies, demonstrating that it consistently outperforms strong baselines in both point prediction and distributional accuracy.