aiqbench analysis
This research advances generative modeling by shifting from discrete time steps to continuous-time evolution on learned data manifolds, enabling temporal super-resolution for video and scientific dynamics. By leveraging pretrained score-based models as geometric priors, the method achieves robust trajectory generation without requiring explicit simulation of the underlying vector field. The approach demonstrates that respecting the intrinsic geometry of score-induced paths provides a strong foundation for stochastic continuous-time generative tasks.
Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds
arXiv:2609.17901v1 Announce Type: cross Abstract: Generative modeling of time-dependent data is typically formulated on a discrete temporal grid, restricting supervision to the observed timestamps in the training data. We instead frame generation as continuous-time evolution on a learned data manifold. To this end, we leverage pretrained score-based models as geometric priors and learn a vector field that evolves data along score-induced interpolation paths. Because these dynamics follow transitions that respect the geometry learned by the score model, they support generation at arbitrary timestamps and temporal super-resolution beyond the discretization of the training data. Moreover, this geometric formulation allows us to train the vector field simulation-free through a regression objective. To improve long-horizon rollout robustness, we introduce an objective that promotes path-relative transverse exponential stability. While motivated by stability theory, it admits a practical interpretation as denoising score matching transverse to the interpolation path. Further, we extend the framework to a probabilistic setting that models a distribution over plausible future trajectories. We demonstrate the method on natural video and scientific dynamical data, including temporal super-resolution, PDE-based spatiotemporal fields, and molecular dynamics. Our results show that score-based priors provide a strong foundation for learning stochastic continuous-time generative dynamics.
Abstract:Generative modeling of time-dependent data is typically formulated on a discrete temporal grid, restricting supervision to the observed timestamps in the training data. We instead frame generation as continuous-time evolution on a learned data manifold. To this end, we leverage pretrained score-based models as geometric priors and learn a vector field that evolves data along score-induced interpolation paths. Because these dynamics follow transitions that respect the geometry learned by the score model, they support generation at arbitrary timestamps and temporal super-resolution beyond the discretization of the training data. Moreover, this geometric formulation allows us to train the vector field simulation-free through a regression objective. To improve long-horizon rollout robustness, we introduce an objective that promotes path-relative transverse exponential stability. While motivated by stability theory, it admits a practical interpretation as denoising score matching transverse to the interpolation path. Further, we extend the framework to a probabilistic setting that models a distribution over plausible future trajectories. We demonstrate the method on natural video and scientific dynamical data, including temporal super-resolution, PDE-based spatiotemporal fields, and molecular dynamics. Our results show that score-based priors provide a strong foundation for learning stochastic continuous-time generative dynamics.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2609.17901 [cs.LG]
(or arXiv:2609.17901v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.17901 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 288 words
