ChronoSync: Recovering Long-Horizon Coupled Dynamics via Cross-Field Synchronization of Decoupled Diffusion Models

Long-horizon prediction of coupled multiphysics PDEs is challenging even when fully coupled trajectories are available for training. We study a harder setting in which the target joint dynamics are unavailable during training and only decoupled conditional trajectories for individual physical fields are observed. We introduce ChronoSync, an inference algorithm that recovers coupled dynamics by synchronizing independently trained conditional Elucidated Rolling Diffusion Models. ChronoSync sequentially composes field-wise probability flows within each denoising step using operator splitting, while a rolling temporal window propagates the synchronized state over long PDE time horizons. We characterize the local composition perturbation through Lie brackets and derive a recursive bound for its propagation across rollouts. Under a mixed regime which allows for varying degrees of local rollout stability in the perturbations, we show that the long-horizon splitting error can remain bounded. We evaluate ChronoSync on FitzHugh–Nagumo, viscous Burgers, Darcy transport, and Rayleigh–B'enard convection, spanning increasingly complex multiphysics interactions from bidirectional linear coupling to nonlinear transport, density-driven flow, and buoyancy–advection feedback under incompressibility. Across these case studies, ChronoSync recovers close to 90% of the conditional to joint oracle error gap on average and is generally the best decoupled data method, substantially approaching models trained directly on coupled trajectories. ChronoSync additionally recovers physically meaningful coupled observables, closely tracking solute transport in Darcy flow and convective heat transport in Rayleigh-B'enard convection. These results demonstrate that long-horizon coupled dynamics can be recovered from decoupled generative models by synchronizing their probability flows across diffusion time and propagating that synchronization coherently across PDE time.