DNS-Calibrated Local Stochastic Transition Closure for PDE-Free Long-Horizon Turbulence Diffusion

PDE-free latent diffusion models can synthesize plausible turbulence fields, but visually realistic snapshots do not guarantee statistically reliable long-horizon rollouts. In CNF-based turbulence diffusion, we observe that long rollouts can drift in latent transition laws, temporal memory, and transport-sensitive diagnostics even when the decoder remains spatially expressive. We address this failure mode with a DNS-calibrated stochastic transition closure for long-horizon turbulence diffusion. The closure is fit offline in a coarse latent observable space and defines stochastic transition tubes calibrated from DNS-referenced latent trajectories. During diffusion training, the frozen closure regularizes the denoiser's predicted-clean latent transitions by penalizing deviations from these calibrated tubes, while leaving the CNF decoder and reverse diffusion sampler unchanged. The method is fully PDE-free, uses no PDE residual or sampling-time correction, and is designed to improve transition-side temporal reliability rather than to serve as a universal physical simulator. Across DNS-referenced long-horizon protocols, the proposed method yields targeted gains in temporal transport and memory diagnostics, especially in high-drift regimes, while decoded-field spectra and derivative-sensitive quantities are reported as physical-fidelity guardrails rather than uniformly optimized targets. These results support stochastic transition closure as a lightweight mechanism for improving the temporal reliability of PDE-free turbulence diffusion.