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Heavy-Tailed Flow Matching via Random Clocks

arXiv cs.LG Multimodal & Generative Zhouhao Yang, Yezhen Wang, Kenji Kawaguchi, Vladimir Braverman, Haoyang Cao 2026-07-15

TL;DR — HTFM (Heavy-Tailed Flow Matching via Random Clocks) is a generative modeling framework that replaces the usual Gaussian source in diffusion/flow-matching with a clock-conditioned Gaussian mixture, letting models better fit heavy-tailed data where rare events matter (imbalanced images, financial returns, weather extremes).

Represents heavy-tailed sources as mixtures of clock-conditioned Gaussians; marginalizing over the clock yields Gaussian scale mixtures spanning Gaussian, α-stable, and Student-t families.
Encodes the path-valued "clock" via truncated logsignature features so the velocity field adapts to the conditional space with negligible overhead.
Reports gains in mode coverage, sample quality, and tail-statistic recovery on 2D imbalanced α-stable mixtures, CIFAR10-LT, and HRRR weather fields versus Gaussian flow matching and heavy-tailed baselines, keeping low-NFE sampling.
Offers a tail-control interface: adjusting only the clock law or tail parameter calibrates generated tail "heaviness" across distribution families.

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