Counterfactual Probabilistic Diffusion with Expert Models

TL;DR

This paper introduces ODE-Diff, a diffusion-based framework that integrates expert models with data-driven methods to improve counterfactual distribution prediction in complex systems, especially under data scarcity.

Contribution

It presents a novel approach combining mechanistic and data-driven modeling using diffusion processes guided by expert signals for better causal inference.

Findings

Outperforms baseline models in COVID-19 simulations

Achieves higher accuracy in pharmacological dynamics

Demonstrates reliable results on real-world case studies

Abstract

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.