# Interventional Flow Matching: Prospective Dose-Response Forecasting with Velocity-Field Jacobian Regularization

arXiv: https://arxiv.org/abs/2606.29386 · HTML: https://mlsanity.com/paper/2606.29386/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 21 of 21)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
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- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Temporal Convolutional Networks: A Unified Approach to Action Segmentation](https://mlsanity.com/paper/1608.08242/) (2016)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
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- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [Causal Regularization](https://mlsanity.com/paper/1906.12179/) (2019)
- [Learning Insulin-Glucose Dynamics in the Wild](https://mlsanity.com/paper/2008.02852/) (2020)
- [Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator](https://mlsanity.com/paper/2206.07680/) (2022)
- [Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Response](https://mlsanity.com/paper/2402.17233/) (2024)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Graph-Conditional Flow Matching for Relational Data Generation](https://mlsanity.com/paper/2505.15668/) (2025)
- [The Driver-Blindness Phenomenon: Why Deep Sequence Models Default to Autocorrelation in Blood Glucose Forecasting](https://mlsanity.com/paper/2511.20601/) (2025)
- [DiM-Gestor: Co-Speech Gesture Generation with Adaptive Layer Normalization Mamba-2](https://mlsanity.com/paper/2411.16729/) (2024)
- [The Stationarity Bias: Stratified Stress-Testing for Time-Series Imputation in Regulated Dynamical Systems](https://mlsanity.com/paper/2602.15637/) (2026)

## Abstract (arXiv)

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.