Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations.
The paper proposes a continuous‑time generative framework that models time‑dependent data as evolution on a learned data manifold. By using pretrained score‑based models as geometric priors, it learns a vector field that drives data along score‑induced interpolation paths, enabling generation at arbitrary timestamps and temporal super‑resolution. The method includes a regression‑based training objective, a stability‑promoting term interpreted as denoising score matching, and a probabilistic extension for future trajectory distributions, demonstrated on natural video, PDE‑based fields, and molecular dynamics.
By Jan Tauberschmidt, Brian B. Moser, Stanislav Frolov, Andreas Dengel, Andrew B. Duncan, Sebastian J. Vollmer
arXiv:2609.15643v1 Announce Type: new
Abstract: Flow-matching diffusion models have recently emerged as a strong paradigm for high-fidelity visual generation. However, their prohibitively high fine-t...
By Jiayang Gu, Zheng Fang, Lichaun Xiang, Fanghui Liu, Xu Cai, Hongkai Wen
High-fidelity image generation faces a trade-off between speed and quality. Diffusion models produce strong visuals but require costly iterative sampling.
arXiv:2607. 21427v1 Announce Type: new Abstract: Discrete flow matching provides a flexible framework for generative modeling on discrete structures.
By Daniil Cherniavskii, Daniel Severo, Karen Ullrich
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
By Andrew Gracyk