Predicting Unseen Scientific Interactions: Conditional Flow Models Hallucinate Non-Additive Effects

We introduce Prior-Fitted Functional Flows, a generative foundation model for pharmacokinetics that enables zero-shot population synthesis and individual forecasting without manual parameter tuning. We learn functional vector fields, explicitly conditioned on the sparse, irregular data of an entire study population. This enables the generation of coherent virtual cohorts as well as forecasting of partially observed patient trajectories with calibrated uncertainty. We construct a new open-access literature corpus to inform our priors, and demonstrate state-of-the-art predictive accuracy on extensive real-world datasets.

Studying the spatiotemporal evolution of scientific phenomena often relies on costly simulations and experiments. Machine learning-based surrogate models reduce this cost, but most are limited to deterministic forward prediction. Scientific temporal analysis often requires both forward prediction and backward inference, while temporal evolution is not always uniquely determined, especially for the inverse problem. We introduce DiffUNet^2, a bidirectional conditional diffusion model for probabilistic scientific temporal prediction. It supports both forward and backward prediction within a shared model. We evaluate DiffUNet^2 on four scientific temporal datasets spanning fluid dynamics, chemical reaction dynamics, and material deformation, against deterministic and probabilistic baselines. Results show that DiffUNet^2 achieves strong predictive performance in both temporal directions and high probabilistic ensemble quality compared with existing baselines. To support practical scientific exploration beyond prediction, we further extend DiffUNet^2's generation ability with target-guided state editing, allowing states of interest to be specified and explored in both temporal directions.

Many scientific questions require reasoning about what was never observed: What if the conditions, interventions, or history had been different? Models can predict accurately on observed data yet fail on such what-if queries when correlated inputs are varied independently. A common remedy is to add controlled simulation data in which these factors are explicitly disentangled, but this requires access to a simulator, can be computationally expensive, and inherits the simulator's modeling assumptions. We introduce ReRoute, a framework for targeted scientific what-if prediction that combines factual data with partial mechanistic knowledge, without requiring controlled intervention data for adaptation. ReRoute fixes the queried input of a pretrained backbone to a reference value, reintroduces its variation through a known mechanistic pathway, and fine-tunes on the original factual data, while leaving downstream effects to the learned dynamics. We provide a causal identification result for this construction under explicit structural assumptions, with the core argument machine-checked in Lean. After showing that ReRoute achieves highly accurate counterfactual predictions in a controlled advection-diffusion system where exact responses are available, we turn to state-of-the-art climate emulation. On held-out coupled-climate interventions, ReRoute reduces aggregate climate error by 18.2-31.8% under severe CO$_2$ distribution shifts while preserving skill under standard conditions, at a small fraction of the cost of retraining on additional controlled simulations, without even accounting for the substantial expense of generating such data. Finally, on an emulator trained from historical ERA5 reanalysis, where no counterfactual reference exists, ReRoute preserves substantially more of the surface warming implied by the observed boundary conditions under a fixed-CO$_2$ counterfactual.