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MissPath-FM: Flow Matching with Structured Priors for Partially Observed Time Series

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Flow matching and flow sampling

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Proposes MissPath-FM, a flow matching framework for partially observed time series that uses an interpolation or GP-posterior source prior and a missingness-aware smooth path so transport concentrates on missing entries, evaluated on imputation, forecasting, and generation against eight baselines.

Problem

Standard conditional flow matching starts from an uninformed Gaussian source, wasting capacity transporting already-observed entries when imputing or forecasting partially observed time series.

Approach

Replace the Gaussian source with an observation-aware prior (linear interpolation with small observed-entry variance, or a GP posterior) and use an entry-wise power-schedule path (s_obs=2, s_miss=1) so observed entries lock in early and the velocity field concentrates on missing entries.

Key results

• MissPath-FM wins 29 of 32 imputation settings at T=48 (MAE) and 45 of 48 settings overall across T in {24,48,96}.
• Interpolation prior plus flow reduces MAE by 43%-85% under MCAR; the missingness-aware path adds a consistent 12%-26%.
• Structured priors shorten observed-region transport about 15x (miss-to-obs arc-length ratio 19.2x vs 1.1x for Gaussian).

Surprising findings

• Interpolation-only prior is worse than Gaussian+Flow under block missingness on Electricity (MAE 0.842 vs 0.414), so the prior alone can be harmful.
• Adding raw observed values as extra network input slightly degrades performance once the structured prior encodes observations.

Limitations

• Advantage shrinks at very sparse observation (90% missingness) and under observation noise above about 0.2-0.3 z-scored units; falls behind SAITS on some settings.
• GP prior is per-variable, ignores cross-variable dependencies, and its cost grows cubically in D.
• Largest tested setting is D=36 and T=192; scaling behavior not established.

Experimental setup

Datasets: Synthetic ETTm1 Electricity PhysioNet 2012

Benchmarks: ETTm1 Synthetic Electricity PhysioNet 2012

Metrics: MAE CRPS ACE Interval Score 90 Energy Score discriminative score predictive score spectral distance

Baselines: SAITS BRITS CSDI GP-VAE FlowTS CLWF TSFlow PSW-I

Builds on: conditional flow matching rectified flow OT-CFM TSFlow CSDI

Closest papers by meaning

• PrismFlow: Residual Dynamics for Flow Matching in Time-Series Generation (NeurIPS 2026 · similarity 0.89)
• Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment (CVPR 2025 · similarity 0.89)
• Structured Coupling for Flow Matching (NeurIPS 2026 · similarity 0.89)
• Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting (ICLR 2025 · similarity 0.89)
• SDFlow: Similarity-Driven Flow Matching for Time Series Generation (NeurIPS 2026 · similarity 0.89)
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