arXiv:2610. 02663v1 Announce Type: cross Abstract: Despite the remarkable empirical success of flow-matching models, their statistical generalization guarantees remain underdeveloped.
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.
arXiv:2606. 16610v1 Announce Type: cross Abstract: Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood.
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...
arXiv:2610.07655v1 Announce Type: cross Abstract: Discrete diffusion models have emerged as a practically successful framework for generative modeling on discrete product spaces, yet their statistica...
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.
arXiv:2609.38049v1 Announce Type: new Abstract: Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite...
Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FF...
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
arXiv:2605. 12951v2 Announce Type: replace-cross Abstract: We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution.
arXiv:2609.38547v1 Announce Type: cross Abstract: Defining a weighted mean over probability measures under probability metrics is a central tool in probabilistic machine learning. Under the Wasserste...
arXiv:2609. 11521v2 Announce Type: replace Abstract: Score matching avoids computing the normalising constant that maximum-likelihood estimation requires.
The paper investigates when conditional flow matching (CFM) can replace pointwise negative log-likelihood (NLL) calculations. It shows that for linear Gaussian paths, the endpoint NLL can be exactly decomposed into entropy, a weighted CFM objective, and residual terms, meaning CFM-only estimates are exact only when these residuals cancel. The study finds that ordinary CFM is generally not a pointwise NLL estimator, and even weighted variants may not fully eliminate bias, especially in training or on‑policy settings, with experiments confirming these theoretical insights.