Heavy-Tailed Flow Matching via Random Clocks

• URL: http://arxiv.org/abs/2607.13841v1
• Date: Wed, 15 Jul 2026 13:48:05 GMT
• Title: Heavy-Tailed Flow Matching via Random Clocks
• Abstract summary: Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes.<n>We propose Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that portrays heavy-tailed sources as mixtures of clock-conditioned Gaussian sources.
• Score: 52.78194016835051
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes. Standard diffusion and flow-matching models typically begin from Gaussian noise or Gaussian source distributions, which yield tractable training targets but provide a poor inductive match for heavy-tailed data. We propose Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that portrays heavy-tailed sources as mixtures of clock-conditioned Gaussian sources. Conditioning on a given clock path, the source distribution and flow are Gaussian; marginalizing over the clock gives a Gaussian scale mixture covering Gaussian, $α$-stable, and Student-t families. To make the clock-conditioned vector field practical, we encode the path-valued clock using truncated logsignature features, allowing the velocity field to adapt to the realized conditional space with negligible overhead. Empirically, on 2D imbalanced $α$-stable mixtures, CIFAR10-LT, and HRRR weather fields, HTFM improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and competitive heavy-tailed baselines, while retaining the low-NFE sampling advantage of flow matching. Moreover, the random-clock formulation further provides a practical tail-control interface: by varying only the clock law or tail parameter, the same architecture can calibrate the ``heaviness'' of generated tails across different distribution families.

Related papers

• Fluid-DiT: Graph-Free Diffusion Transformers for Fluid Flow Simulations Learning [50.053186229257555]
  We propose a Graph-Free Diffusion Transformer that replaces graph message passing with attention-based denoising.<n>By leveraging the transformer's global receptive field, Fluid-DiT naturally captures both local flow structures and long-range correlations.<n>It consistently outperforms graph-based diffusion baselines in both sample quality and distributional accuracy.
  arXiv  Detail & Related papers  (2026-08-07T12:28:45Z)
• LC-GRPO: Bridging Train-Inference Gap for Flow-Based GRPO with Langevin Correction [59.32834240526981]
  Flow-based generative models are typically sampled by solving a deterministic ordinary differential equation (ODE)<n>Existing GRPO methods for flow models replace the Euler-time ODE with aotropic differential equation (SDE) during training.<n>We introduce LC-GRPO, a flow-based GRPO framework with Langevin correction targeting the marginal distribution at the resulting timestep.
  arXiv  Detail & Related papers  (2026-08-06T04:47:57Z)
• Simplifying Flow Matching Transformations with Low-Rank Mixture Models [58.797704398690165]
  We propose using mixtures of probabilistic principal component analyzers (MPPCA) as the latent density for normalizing flows.<n>We simplify the learned flow transformation by learning a latent distribution that more closely aligns with the data distribution in terms of KL divergence.<n>MPPCA models can be fit quickly and cheaply using the expectation-maximization algorithm, making them a practical choice for initializing latent distributions even in high-dimensional generative tasks.
  arXiv  Detail & Related papers  (2026-06-29T03:03:06Z)
• Coreset-Induced Conditional Velocity Flow Matching [4.297295761793895]
  We propose a generative model that augments hierarchical rectified flow with a data-informed source distribution.<n>Key observation is that this inner source can be replaced by a closed-form surrogate built from a coreset of the target.<n>A lightweight correction flow, trained from this exact surrogate source, then refines the remaining surrogate-to-target residual.
  arXiv  Detail & Related papers  (2026-05-13T03:34:40Z)
• MixFlow: Mixed Source Distributions Improve Rectified Flows [18.451270798004344]
  Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images.<n>They are hindered by slow iterative sampling caused by the highly curved generative paths they learn.<n>We present MixFlow, a training strategy that reduces the generative path curvatures and considerably improves sampling efficiency.
  arXiv  Detail & Related papers  (2026-04-10T10:06:15Z)
• Fast Sampling for Flows and Diffusions with Lazy and Point Mass Stochastic Interpolants [5.492889521988414]
  We prove how to convert a sample path of a differential equation (SDE) with arbitrary diffusion coefficient under any schedule.<n>We then extend the interpolant framework to admit a larger class of point mass schedules.
  arXiv  Detail & Related papers  (2026-02-03T17:48:34Z)
• Scale-Adaptive Generative Flows for Multiscale Scientific Data [20.583125441867434]
  Flow-based generative models can face challenges when modeling scientific data with multiscale Fourier spectra.<n>Key insight is that the noise should not be smoother than the target data, to ensure bounded drift fields near the initial time.<n>We show that spectrum-matched noise improves numerical efficiency compared to standard white-noise approaches.
  arXiv  Detail & Related papers  (2025-09-03T03:17:49Z)
• Gaussian Mixture Flow Matching Models [63.092956669059824]
  Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models re parameterize the Gaussian mean as flow velocity.<n>They underperform in few-step sampling due to discretization error and tend to produce over-saturated colors under classifier-free guidance (CFG)<n>We introduce a novel probabilistic guidance scheme that mitigates the over-saturation issues of CFG and improves image generation quality.
  arXiv  Detail & Related papers  (2025-04-07T17:59:42Z)
• Stream-level flow matching with Gaussian processes [4.935875591615496]
  Conditional flow matching (CFM) is a family of training algorithms for fitting continuous normalizing flows (CNFs)<n>We extend the CFM algorithm by defining conditional probability paths along streams'', instances of latent paths that connect data pairs of source and target.<n>We show that this generalization of the CFM can effectively reduce the variance in the estimated marginal vector field at a moderate computational cost.
  arXiv  Detail & Related papers  (2024-09-30T15:47:22Z)
• Marginalization Consistent Probabilistic Forecasting of Irregular Time Series via Mixture of Separable flows [4.489135297410294]
  Probabilistic forecasting models for joint distributions of targets in irregular time series with missing values are a heavily under-researched area in machine learning.<n>We propose MOSES (Marginalization Consistent Mixture of Separable Flows), a model that parametrizes a mixture of several latent Gaussian processes combined with separable uni- normality flows.<n>Experiments on four datasets show that MOSES achieves both accurate joint and marginal predictions, surpassing all other marginalization consistent baselines, while only trailing slightly behind ProFITi in joint prediction, but vastly superior when predicting marginal distributions.
  arXiv  Detail & Related papers  (2024-06-11T13:28:43Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.