Functional Flow Matching
This work addresses generative modeling for function spaces, which is important for applications like signal processing or physics simulations, but it appears incremental as it builds on the recently-introduced Flow Matching model.
The authors tackled the problem of generative modeling in infinite-dimensional function spaces by proposing Functional Flow Matching (FFM), which generalizes Flow Matching to operate without likelihoods or simulations, and demonstrated that FFM outperforms other function-space generative models on real-world benchmarks.
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.