This paper presents a method for predicting counterfactual distributions in complex dynamic systems, which are essential for scientific modeling and decision-making in fields such as public health and medicine. Existing methods tend to rely on point estimates or purely data-driven models, which are prone to errors when data is scarce. In this paper, we propose a time-series diffusion-based framework that extracts high-dimensional signals from incomplete expert models and utilizes them as structured prior information for generative models. This method, called ODE-Diff, bridges mechanistic and data-driven approaches, enabling more reliable and interpretable causal inference. We evaluate ODE-Diff using semi-synthetic COVID-19 simulations, synthetic pharmacodynamics, and real-world case studies, and find that it consistently outperforms robust baseline models in both point-prediction and distributional accuracy.
