Functional Flow Matching

• URL: http://arxiv.org/abs/2305.17209v2
• Date: Tue, 5 Dec 2023 19:53:12 GMT
• Title: Functional Flow Matching
• Authors: Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth
• Abstract summary: We propose a function-space generative model that generalizes the recently-introduced Flow Matching model. Our method does not rely on likelihoods or simulations, making it well-suited to the function space setting. We demonstrate through experiments on several real-world benchmarks that our proposed FFM method outperforms several recently proposed function-space generative models.
• Score: 14.583771853250008
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate 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 several real-world benchmarks that our proposed FFM method outperforms several recently proposed function-space generative models.

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