Two-Sample Testing via Generative Processes
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
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.