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

arXiv: https://arxiv.org/abs/2610.17715 · HTML: https://mlsanity.com/paper/2610.17715/

## 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 32 references that are in the map.
- First posted on arXiv 13 Oct 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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)
- [Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputation](https://mlsanity.com/paper/2305.07247/) (2023)
- [Trajectory Flow Matching with Applications to Clinical Time Series Modeling](https://mlsanity.com/paper/2410.21154/) (2024)
- [TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generation](https://mlsanity.com/paper/2408.06672/) (2024)
- [CFMI: Flow Matching for Missing Data Imputation](https://mlsanity.com/paper/2506.09258/) (2025)
- [Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching](https://mlsanity.com/paper/2507.07192/) (2025)
- [Conditional Lagrangian Wasserstein Flow for Time Series Imputation](https://mlsanity.com/paper/2410.07550/) (2024)
- [Impute-MACFM: Imputation based on Mask-Aware Flow Matching](https://mlsanity.com/paper/2509.23126/) (2025)

## Abstract (arXiv)

Flow matching has emerged as a powerful alternative to diffusion models for generative modeling, but standard conditional flow matching is fundamentally misaligned with partially observed time series: starting from an uninformed Gaussian source forces the model to transport even already-observed entries from noise to the target, wasting capacity on trivially known regions. We propose MissPath-FM, a partial-observation-aware flow matching framework that redesigns the source prior and probability path for incomplete time series. MissPath-FM employs structured source priors (interpolation priors and Gaussian process posterior priors) to initialize the flow close to the observed signal, paired with a missingness-aware smooth path that allocates transport asymmetrically between observed and missing regions. We evaluate systematically across four datasets, four missingness mechanisms (MCAR, block, MNAR, irregular), two missing ratios, and three sequence lengths (T in {24, 48, 96}), totaling 48 settings against eight baselines. MissPath-FM wins 29 of 32 settings at T=48 and 45 of 48 overall (93.8%). Our ablations reveal a regime-dependent design hierarchy in which no single component suffices: under random missingness the source prior yields a large initial gain, but under structured block missingness it can fail entirely and the learned flow becomes indispensable; the missingness-aware path contributes a further 12%-26% across all regimes. Mechanistically, structured priors shorten observed-region transport by up to 15x, concentrating the velocity field on genuinely uncertain entries. Project page: https://zgp110.github.io/misspath-fm/