Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points

Justin Lee, Behnaz Moradijamei, Heman Shakeri
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:33476-33498, 2025.

Abstract

Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality reduction techniques, which can oversimplify the dynamics and fail to capture critical transient behaviors in non-equilibrium systems. We present Multi-Marginal Stochastic Flow Matching (MMSFM), a novel extension of simulation-free score and flow matching methods to the multi-marginal setting, enabling the alignment of high-dimensional data measured at non-equidistant time points without reducing dimensionality. The use of measure-valued splines enhances robustness to irregular snapshot timing, and score matching prevents overfitting in high-dimensional spaces. We validate our framework on several synthetic and benchmark datasets, including gene expression data collected at uneven time points and an image progression task, demonstrating the method’s versatility.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-lee25x, title = {Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points}, author = {Lee, Justin and Moradijamei, Behnaz and Shakeri, Heman}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {33476--33498}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/lee25x/lee25x.pdf}, url = {https://proceedings.mlr.press/v267/lee25x.html}, abstract = {Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality reduction techniques, which can oversimplify the dynamics and fail to capture critical transient behaviors in non-equilibrium systems. We present Multi-Marginal Stochastic Flow Matching (MMSFM), a novel extension of simulation-free score and flow matching methods to the multi-marginal setting, enabling the alignment of high-dimensional data measured at non-equidistant time points without reducing dimensionality. The use of measure-valued splines enhances robustness to irregular snapshot timing, and score matching prevents overfitting in high-dimensional spaces. We validate our framework on several synthetic and benchmark datasets, including gene expression data collected at uneven time points and an image progression task, demonstrating the method’s versatility.} }
Endnote
%0 Conference Paper %T Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points %A Justin Lee %A Behnaz Moradijamei %A Heman Shakeri %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-lee25x %I PMLR %P 33476--33498 %U https://proceedings.mlr.press/v267/lee25x.html %V 267 %X Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality reduction techniques, which can oversimplify the dynamics and fail to capture critical transient behaviors in non-equilibrium systems. We present Multi-Marginal Stochastic Flow Matching (MMSFM), a novel extension of simulation-free score and flow matching methods to the multi-marginal setting, enabling the alignment of high-dimensional data measured at non-equidistant time points without reducing dimensionality. The use of measure-valued splines enhances robustness to irregular snapshot timing, and score matching prevents overfitting in high-dimensional spaces. We validate our framework on several synthetic and benchmark datasets, including gene expression data collected at uneven time points and an image progression task, demonstrating the method’s versatility.
APA
Lee, J., Moradijamei, B. & Shakeri, H.. (2025). Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:33476-33498 Available from https://proceedings.mlr.press/v267/lee25x.html.

Related Material