arXiv:2607. 04442v1 Announce Type: cross Abstract: Diffusion models (DMs) are a state-of-the-art generative method to approximately sample from an unknown distribution.
The paper introduces a method for creating generative diffusion surrogates that use an analytically derived variance schedule based on the time derivative of known variance from macroscopic theory or empirical scaling. By enforcing this variance path, the model can capture non‑Gaussian structure in transport systems without requiring intermediate‑time physical data. The approach is validated on ballistic‑to‑diffusive transport in turbulent plasmas, accurately reproducing test‑particle distributions, laboratory‑measured variance, and simulated kurtosis evolution.
arXiv:2507. 12843v3 Announce Type: replace Abstract: Are two distributions close to each other with statistical significance?
This paper introduces random-bridges—stochastic processes conditioned to hit target distributions at fixed times—as stochastic transports for generative modeling. Random-bridges can be Markovian or non‑Markovian, continuous or discontinuous, depending on the driving process, and the authors develop both theoretical foundations and practical training/simulation algorithms for Gaussian and Lévy (Gamma, Poisson, Stable‑1/2) bridges. Empirical results on the Gaussian case show that the proposed framework produces high‑quality samples with competitive Fréchet Inception Distance scores relative to popular denoising diffusion and flow‑matching methods.
The paper investigates how kernel-based metrics like KID and KAD perform as two‑sample tests on real embeddings of symbolic music, audio, and images. By applying mean shifts, isotropic contractions, and rotations to one sample, the authors find that the default kernels often fail to detect rotations at 780 samples per side, while they reliably detect mean shifts. Adjusting kernel bandwidths or using alternative kernels (e.g., narrower Gaussian, Laplace) restores sensitivity, and the authors recommend reporting the sample budget and detectable changes for any reported kernel distance.
arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.
arXiv:2512. 13997v2 Announce Type: replace-cross Abstract: Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions.
arXiv:2606. 06179v1 Announce Type: cross Abstract: Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions.
The article introduces PTED, a Python implementation of a permutation test based on the Energy Distance for two-sample testing in multiple dimensions. PTED uses pairwise distances to compute a test statistic that works in high dimensions, on learned feature representations, and for any data type where a distance can be defined. The authors demonstrate that PTED scales linearly with dimensions and sample size while retaining strong discriminative power, and show it outperforms other multi‑dimensional tests in sensitivity.
arXiv:2610. 20743v1 Announce Type: new Abstract: Many modern learning problems require comparing probability distributions whose individual observations are themselves probability measures, naturally giving rise to meta-measures in $\mathcal{P}(\mathcal{P}(\Omega))$.
arXiv:2607. 15485v1 Announce Type: new Abstract: Score-based generative models exhibit a puzzling behavior: they often appear to cover all modes of a target multimodal distribution and yet may fail to learn the correct relative mode amplitudes, which can be interpreted as mixture weights.
arXiv:2610. 10190v1 Announce Type: cross Abstract: We analyze the first-order deterministic diffusion sampler of Karras et al.