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Generative Modeling of Stochastic Dynamics for Long-Time Evolution

arXiv 2610.00546 ↗First posted 30 Sep 2026cond-mat.stat-mech cs.LG hep-latcited by 0

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Abstract (arXiv)

Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar t1/3 coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.

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References · 20

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
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  8. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  9. 2023DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statisticscited by 161
  10. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 147
  11. 2023Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamicscited by 62
  12. 2023Learning Stochastic Dynamical System via Flow Map Operatorcited by 24
8 more
  1. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  2. 2024A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systemscited by 19
  3. 2024Understanding Diffusion Models by Feynman's Path Integralcited by 13
  4. 2024On learning higher-order cumulants in diffusion modelscited by 10
  5. 2025Generative diffusion model with inverse renormalization group flowscited by 10
  6. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  7. 2026Scalable Spatio-Temporal SE(3) Diffusion for Long-Horizon Protein Dynamicscited by 4
  8. 2025Learning the action for long-time-step simulations of molecular dynamicscited by 2

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