arXiv:2610. 02663v1 Announce Type: cross Abstract: Despite the remarkable empirical success of flow-matching models, their statistical generalization guarantees remain underdeveloped.
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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...