Functional Flow Matching

Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3934-3942, 2024.

Abstract

We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate directly in infinite-dimensional spaces. Our approach works by first defining a path of probability measures that interpolates between a fixed Gaussian measure and the data distribution, followed by learning a vector field on the underlying space of functions that generates this path of measures. Our method does not rely on likelihoods or simulations, making it well-suited to the function space setting. We provide both a theoretical framework for building such models and an empirical evaluation of our techniques. We demonstrate through experiments on synthetic and real-world benchmarks that our proposed FFM method outperforms several recently proposed function-space generative models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-kerrigan24a, title = {Functional Flow Matching}, author = {Kerrigan, Gavin and Migliorini, Giosue and Smyth, Padhraic}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3934--3942}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/kerrigan24a/kerrigan24a.pdf}, url = {https://proceedings.mlr.press/v238/kerrigan24a.html}, abstract = {We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate directly in infinite-dimensional spaces. Our approach works by first defining a path of probability measures that interpolates between a fixed Gaussian measure and the data distribution, followed by learning a vector field on the underlying space of functions that generates this path of measures. Our method does not rely on likelihoods or simulations, making it well-suited to the function space setting. We provide both a theoretical framework for building such models and an empirical evaluation of our techniques. We demonstrate through experiments on synthetic and real-world benchmarks that our proposed FFM method outperforms several recently proposed function-space generative models.} }
Endnote
%0 Conference Paper %T Functional Flow Matching %A Gavin Kerrigan %A Giosue Migliorini %A Padhraic Smyth %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-kerrigan24a %I PMLR %P 3934--3942 %U https://proceedings.mlr.press/v238/kerrigan24a.html %V 238 %X We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate directly in infinite-dimensional spaces. Our approach works by first defining a path of probability measures that interpolates between a fixed Gaussian measure and the data distribution, followed by learning a vector field on the underlying space of functions that generates this path of measures. Our method does not rely on likelihoods or simulations, making it well-suited to the function space setting. We provide both a theoretical framework for building such models and an empirical evaluation of our techniques. We demonstrate through experiments on synthetic and real-world benchmarks that our proposed FFM method outperforms several recently proposed function-space generative models.
APA
Kerrigan, G., Migliorini, G. & Smyth, P.. (2024). Functional Flow Matching. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3934-3942 Available from https://proceedings.mlr.press/v238/kerrigan24a.html.

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