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arXiv Machine Learning By Yang-yang Tan, Jinyang Li, Lingxiao Wang

Generative Modeling of Stochastic Dynamics for Long-Time Evolution

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The paper demonstrates that long‑time stochastic dynamics can be predicted using generative diffusion models trained only on configuration pairs separated by a short, fixed time lag, without requiring the underlying equations of motion. Applied to two‑dimensional Model B and driven colloids in a periodic optical potential, the learned transition kernels accurately reproduce dynamic critical scaling, self‑similar coarsening, and experimental observables such as particle current and mean passage time, even on larger lattices and unseen initial conditions. This shows that short‑time observations contain sufficient information to forecast emergent non‑equilibrium behavior over extended periods.

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