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Trajectory Flow Matching with Applications to Clinical Time Series Modelling
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Proposes Trajectory Flow Matching (TFM), a simulation-free way to train Neural SDEs on irregular clinical time series using flow matching with history conditioning, a target-prediction reparameterization, a time-predictive loss, and a learned uncertainty head.
Problem
Training Neural SDEs for irregularly sampled, stochastic time series currently requires backpropagation through SDE solvers, which is slow and unstable; clinical trajectories also contain intersecting paths that simple models cannot separate.
Approach
Extend conditional flow and bridge matching to trajectories by conditioning the flow on a sliding window of past observations (history memory) and covariates, so that non-crossing coupling is preserved; add a target-prediction parameterization, a time-to-next-observation head, and a learned uncertainty (sigma) head trained without simulation.
Key results
- TFM-ODE reduced MSE versus the best baseline on ICU Sepsis from 4.671e-3 (FM baseline ODE) to 0.793e-3, roughly 83%.
- On ICU Cardiac Arrest, TFM achieved MSE 2.755e-3 versus 3.250e-3 for NeuralSDE; on ICU GIB, TFM achieved 2.596e-3 versus 3.186e-3 for NeuralSDE.
- TFM gave lower uncertainty test MSE than TFM-ODE on all three ICU datasets (e.g. 0.724 vs 1.039 on ICU sepsis) and lower data-variance MMD on ICU GIB and ED GIB.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use TFM-ODE instead of the strongest deterministic baseline | Clinical trajectory modeling · ICU Sepsis | Mean MSE (× 10^-3): 4.671 ± 0.791 -> 0.793 ± 0.017 | Helped |
| use TFM-ODE instead of the strongest deterministic baseline | Clinical trajectory modeling · ICU Cardiac Arrest | Mean MSE (× 10^-3): 6.153 ± 0.000 -> 2.762 ± 0.021 | Helped |
| use TFM-ODE instead of the strongest deterministic baseline | Clinical trajectory modeling · ICU GIB | Mean MSE (× 10^-3): 3.170 ± 0.000 -> 2.673 ± 0.069 | Helped |
| use TFM-ODE instead of the strongest deterministic baseline | Clinical trajectory modeling · ED GIB | Mean MSE (× 10^-3): 10.859 ± 0.000 -> 8.245 ± 0.495 | Helped |
| use TFM instead of NeuralSDE | Clinical trajectory modeling · ICU Sepsis | Mean MSE (× 10^-3): 4.747 ± 0.000 -> 0.796 ± 0.026 | Helped |
| use TFM instead of NeuralSDE | Clinical trajectory modeling · ICU Cardiac Arrest | Mean MSE (× 10^-3): 3.250 ± 0.024 -> 2.755 ± 0.015 | Helped |
| use TFM instead of NeuralSDE | Clinical trajectory modeling · ICU GIB | Mean MSE (× 10^-3): 3.186 ± 0.000 -> 2.596 ± 0.079 | Helped |
| use TFM instead of NeuralSDE | Clinical trajectory modeling · ED GIB | Mean MSE (× 10^-3): 10.850 ± 0.043 -> 8.613 ± 0.260 | Helped |
| use stochastic TFM rather than TFM-ODE | Clinical trajectory modeling · ICU Sepsis, ICU Cardiac Arrest, and ICU GIB | Uncertainty test MSE: 1.039 ± 0.1645 -> 0.724 ± 0.0072; 0.970 ± 0.1426 -> 0.636 ± 0.0024; 0.9843 ± 0.2233 -> 0.605 ± 0.0137 | Helped |
| remove uncertainty prediction (ablation) | TFM-ODE · Clinical trajectory modeling | Mean MSE (× 10^-3): 0.793 ± 0.017 -> 1.170 ± 0.014; 2.762 ± 0.017 -> 2.759 ± 0.015; 2.673 ± 0.069 -> 3.097 ± 0.054; 8.245 ± 0.495 -> 8.659 ± | Hurt |
| remove uncertainty prediction (ablation) | TFM · Clinical trajectory modeling | Mean MSE (× 10^-3): 0.796 ± 0.026 -> 0.816 ± 0.031; 2.596 ± 0.079 -> 2.778 ± 0.021; 2.762 ± 0.021 -> 2.754 ± 0.095; 8.613 ± 0.260 -> 8.600 ± | Mixed |
| add trajectory memory (ablation) | TFM and TFM-ODE · ICU Sepsis and ICU GIB | Mean MSE (× 10^-3): TFM-ODE ICU Sepsis: 1.555 -> 1.170; ICU GIB: 2.981 -> 3.097; TFM ICU Sepsis: 1.965 -> 0.816; ICU GIB: 4.037 -> 2.754 | Helped |
Surprising findings
- Removing the uncertainty prediction head increased test MSE for the trajectory-prediction head, suggesting a synergy between the two flows.
- Adding history memory did not improve performance on the ED GIB dataset, which has sparser measurements.
Limitations
- Memory (history conditioning) helps less in high-frequency or sparse settings such as ED GIB.
- No current capacity to estimate causal representations or handle interventions.
- Coupling preservation guarantees rely on assumptions (A1)-(A3) that may not hold exactly in practice.
Experimental setup
Datasets: eICU Collaborative Research Database v2.0 MIMIC-III ED GIB institutional EHR data (Yale New Haven Hospital) 1D damped harmonic oscillator (synthetic)
Benchmarks: ICU Sepsis ICU Cardiac Arrest ICU GIB ED GIB
Metrics: mean MSE RBF-MMD uncertainty test MSE
Baselines: NeuralODE NeuralSDE Latent NeuralODE Aligned FM FM baseline ODE
Builds on: conditional flow matching neural ODE neural SDE aligned flow matching DEUP
Closest papers by meaning
- SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations (ICML 2025 · similarity 0.90)
- Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions (NeurIPS 2025 · similarity 0.88)
- Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data (ICLR 2024 · similarity 0.88)
- Efficient Training of Neural Stochastic Differential Equations by Matching Finite Dimensional Distributions (ICLR 2025 · similarity 0.87)
- Simulation-Free Training of Neural ODEs on Paired Data (NeurIPS 2024 · similarity 0.86)
- PrismFlow: Residual Dynamics for Flow Matching in Time-Series Generation (NeurIPS 2026 · similarity 0.86)
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