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Functional Flow Matching

Gavin Kerrigan · Giosue Migliorini · Padhraic Smyth

MR1 & MR2 - Number 106
award Student Paper Highlight
[ ]
Sat 4 May 6 a.m. PDT — 8:30 a.m. PDT
Oral presentation: Oral: Deep Learning
Sat 4 May 1:30 a.m. PDT — 2:30 a.m. PDT


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.

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