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

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.

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