Stream-level Flow Matching with Gaussian Processes

Ganchao Wei, Li Ma
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:66137-66154, 2025.

Abstract

Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares regression to the conditional vector field specified given one or both ends of the flow path. In this paper, we extend the CFM algorithm by defining conditional probability paths along "streams”, instances of latent stochastic paths that connect data pairs of source and target, which are modeled with Gaussian process (GP) distributions. The unique distributional properties of GPs help preserve the “simulation-free” nature of CFM training. We show that this generalization of the CFM can effectively reduce the variance in the estimated marginal vector field at a moderate computational cost, thereby improving the quality of the generated samples under common metrics. Additionally, adopting the GP on the streams allows for flexibly linking multiple correlated training data points (e.g., time series). We empirically validate our claim through both simulations and applications to image and neural time series data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wei25i, title = {Stream-level Flow Matching with {G}aussian Processes}, author = {Wei, Ganchao and Ma, Li}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {66137--66154}, 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/wei25i/wei25i.pdf}, url = {https://proceedings.mlr.press/v267/wei25i.html}, abstract = {Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares regression to the conditional vector field specified given one or both ends of the flow path. In this paper, we extend the CFM algorithm by defining conditional probability paths along "streams”, instances of latent stochastic paths that connect data pairs of source and target, which are modeled with Gaussian process (GP) distributions. The unique distributional properties of GPs help preserve the “simulation-free” nature of CFM training. We show that this generalization of the CFM can effectively reduce the variance in the estimated marginal vector field at a moderate computational cost, thereby improving the quality of the generated samples under common metrics. Additionally, adopting the GP on the streams allows for flexibly linking multiple correlated training data points (e.g., time series). We empirically validate our claim through both simulations and applications to image and neural time series data.} }
Endnote
%0 Conference Paper %T Stream-level Flow Matching with Gaussian Processes %A Ganchao Wei %A Li Ma %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-wei25i %I PMLR %P 66137--66154 %U https://proceedings.mlr.press/v267/wei25i.html %V 267 %X Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares regression to the conditional vector field specified given one or both ends of the flow path. In this paper, we extend the CFM algorithm by defining conditional probability paths along "streams”, instances of latent stochastic paths that connect data pairs of source and target, which are modeled with Gaussian process (GP) distributions. The unique distributional properties of GPs help preserve the “simulation-free” nature of CFM training. We show that this generalization of the CFM can effectively reduce the variance in the estimated marginal vector field at a moderate computational cost, thereby improving the quality of the generated samples under common metrics. Additionally, adopting the GP on the streams allows for flexibly linking multiple correlated training data points (e.g., time series). We empirically validate our claim through both simulations and applications to image and neural time series data.
APA
Wei, G. & Ma, L.. (2025). Stream-level Flow Matching with Gaussian Processes. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:66137-66154 Available from https://proceedings.mlr.press/v267/wei25i.html.

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