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Functional Flow Matching
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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.
Forward citations
Cited by 5 Pith papers
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Learning sufficient low-dimensional structures through conditional optimal transport
Sufficiency forces the conditional optimal-transport map and its velocity to factor through the reduced covariate, and the resulting flow-matching estimator (SDR-COT) recovers the central subspace in the linear case.
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Scale-Adaptive Generative Flows for Multiscale Scientific Data
For generative flows on multiscale scientific fields, the noise spectrum should be at least as rough as the data's, and a scale-adaptive schedule can tame the terminal-time stiffness of rougher noise.
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Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation
Post-hoc distillation with a PDE-residual loss on final samples avoids the Jensen gap and yields one-step physics-constrained generation.
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NeuTSFlow: Modeling Continuous Functions Behind Time Series Forecasting
A flow-matching model with a neural-operator velocity field is proposed to forecast time series by transporting distributions over continuous functions, reporting top average rank on eight benchmarks.
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Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching
CGFM uses an auxiliary model's predictions as the source for flow matching to learn forecast residuals and improve time series forecasts.
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