Diffusion Models Calibrated for Stochastic Transport Systems

This research presents a novel application of generative diffusion models as surrogates for stochastic transport systems, particularly those where the variance or mean-square displacement is known from macroscopic theory or empirical scaling, but the complete distributional structure remains elusive. Traditional generative diffusion models, often used in image and audio synthesis, typically employ heuristically chosen noise schedules, lacking a physical time calibration. The key innovation here is to prescribe the forward noising rate as the time derivative of the known variance, effectively transforming the generative time into a calibrated physical transport clock. This ensures that the variance path is enforced by construction. The learned score field then captures how non-Gaussian structures, inherited from initial data, are smoothed along this predefined path, critically requiring no intermediate-time physical transport data for training. The effectiveness of this approach was demonstrated in modeling ballistic-to-diffusive transport in turbulent plasmas. The generative surrogate successfully matched test-particle distributions, accurately reproduced the laboratory-measured variance scale, and tracked the simulated kurtosis evolution without any schedule tuning. This capability opens avenues for calibrated emulation and likelihood-based inference in complex physical systems.