The paper studies how flow‑matching schedules influence sampling dynamics and regression variance. For centered commuting Gaussians, it shows that a direction‑dependent schedule splits into a variance path that determines intermediate laws and a factorization that keeps the flow unchanged while controlling irreducible regression variance. The authors analyze finite‑step Euler accuracy, derive a drift bound for exact N‑step sampling, and provide closed‑form factorizations that either minimize time‑averaged regression variance or keep it constant along a fixed path.
arXiv:2609.39488v1 Announce Type: new Abstract: Flow matching generates samples by gradually transforming noise into data. In practice, using a finite number of sampling steps introduces a numerical...
arXiv:2609.17287v1 Announce Type: new Abstract: In flow matching (FM), a velocity model $v_{\theta}$ is trained using a predefined path $g_t$ that connects data and noise samples (e.g., $g_t(x_0, x_1...
GeoSPRINT is a training‑free framework that constructs non‑uniform sampling schedules for diffusion model inference by detecting geometrically redundant steps in denoising trajectories. It uses a hyperplanarity test in latent space, implemented via QR factorization, to allocate more steps to high‑curvature regions, and introduces the trajectory projection score α_traj as a model‑free diagnostic for flow quality. Across CIFAR‑10, LSUN Church, and Stable Diffusion v1.5, GeoSPRINT consistently outperforms uniform DDIM schedules at matched NFE budgets, improving FID scores by up to 1.93 points.
arXiv:2606. 31063v1 Announce Type: cross Abstract: Gaussian process inference is often limited by cubic computational costs, a challenge that becomes more pronounced in spatio-temporal settings where posterior inference is required over dense grids.
The paper introduces Difficulty-Calibrated Flow Matching, a method that adapts the noise-to-data interpolation schedule in Conditional Flow Matching based on a pilot run’s loss profile. By setting the schedule to the quantile function of this difficulty profile, the training trajectory spends more time where the velocity is hardest to learn. Experiments on CIFAR-10, MNIST, and Fashion‑MNIST show that this calibrated path achieves the best FID on CIFAR‑10 and outperforms all fixed schedules in large‑batch, few‑update settings, where compute is most limited.
arXiv:2607. 28864v1 Announce Type: cross Abstract: Tree-based diffusion models fit flexible conditional predictive distributions for tabular regression without a neural density estimator, but they inherit their design defaults---noising path, parameterization, training distribution, features, sampler---from the neural setting.
Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data, and the number of network evaluations~(NFE) sets the cost of sampling. The straight-line interpolant carries an implicit choice: the sample moves at constant speed throughout the trajectory.
arXiv:2607. 26285v1 Announce Type: cross Abstract: Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees.
arXiv:2605. 00941v4 Announce Type: replace Abstract: Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem.
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.
arXiv:2607. 13841v1 Announce Type: new Abstract: Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes.
arXiv:2609.38918v1 Announce Type: cross Abstract: Flow Matching (FM) learns a velocity field whose ODE transports a simple source distribution to a target law. Existing finite-sample theory largely t...