arXiv:2609.25659v1 Announce Type: new
Abstract: Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: d...
By Doron Haviv, Edward De Brouwer, Rishabh Anand, Rex Ying, A\"icha Bentaieb, Gabriele Scalia, Hector Corrada Bravo
arXiv:2510. 22778v3 Announce Type: replace-cross Abstract: We develop a free-probabilistic framework for denoising diffusion, in which the data is a self-adjoint operator and its law a spectral distribution.
By Swagatam Das
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.
By Marta Gentiloni Silveri, Giovanni Conforti, Alain Durmus
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.
By Ziyu Chen, Markos A. Katsoulakis, Benjamin J. Zhang
RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.
By Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn, Minhyuk Sung
arXiv:2602. 22265v2 Announce Type: replace Abstract: Modern vision generators transport a base distribution to data through time-indexed measures, implemented as deterministic flows (ODEs) or stochastic diffusions (SDEs).
By Chika Maduabuchi