Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds

2026-09-15

AI Summary

该研究通过在学习的数据流形上使用连续时间生成动力学，利用预训练的基于分数的模型作为几何先验，并学习向量场以沿分数诱导插值路径演化数据，解决了时间依赖数据生成中的离散时间网格限制问题。

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.

Problem

• Continuous-time
• Generative Modeling
• Data Manifold
• Score-based Models
• Temporal Super-resolution

Innovation

• continuous-time generative dynamics
• score-based models
• vector field
• temporal super-resolution
• stochastic continuous-time