Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokinetics
Authors: César Ojeda, Niklas Hartung, Wilhelm Huisinga, Tim Jahn, Purity Kamene Kavwele, Marian Klose, Piyush Kumar, Ramsés J. Sánchez, +1 more
Organizations: University of Potsdam, Germany · Technical University Berlin, Germany · Freie Universität Berlin, Germany · University of Bonn, Germany · NHETC, Rutgers University
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.
Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized from data-supported states rather than from noise. The framework can utilize any pretrained flow model. We develop two probability-preserving sampling mechanisms, a corrected Langevin dynamics with a Metropolis adjustment and a predictor-corrector flow, that operate directly on existing checkpoints. We validate the framework on a synthetic Swiss-roll target, ImageNet-256 and Oxford Flowers-102, where our samplers consistently improve over the original generation procedures.
Eshed Gal, Md Shahriar Rahim Siddiqui, Moshe Eliasof +1
Predicting a patient's physiological trajectory under a planned treatment sequence is a prospective interventional problem, not standard time-series extrapolation. We study this problem in glucose management, where insulin and carbohydrate records are policy-dependent: future drivers are coupled to patient state, behavior, and clinical decision rules, so observational forecasting accuracy alone does not guarantee correct responses to planned interventions. We introduce Interventional Flow Matching (IFM), a continuous-time generative framework for physiologically constrained prospective forecasting. IFM conditions a flow-matching velocity field on patient history and planned future drivers in a bounded latent glucose space. Rather than embedding strict mechanistic glucose--insulin ODE equations or enforcing causality through rollout-based simulations, IFM uses a solver-free regularization: it penalizes the Jacobian of the instantaneous velocity field with respect to smoothed treatment drivers. This imposes signed, dose-bounded local sensitivities directly on the learned dynamics: insulin lowers glucose, carbohydrates raise it, and both responses remain within plausible ranges. On a simulated UVA/Padova type 1 diabetes cohort, IFM achieves the strongest balance between observed-driver RMSE and interventional response metrics. Across experiments, it consistently produces physiologically correct responses to both insulin and carbohydrate drivers while maintaining high directional, and ranking consistency.
Amirreza Dolatpour Fathkouhi, Justin Lee, Heman Shakeri
We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and \revise{cumulative} parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction \revise{instantiation}. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.