Reframing Generative Models for Physical Systems using Stochastic Interpolants

TL;DR

This work introduces stochastic interpolants as a direct, source-to-target generative framework for physical systems, addressing the limitations of Gaussian-prior diffusion in autoregressive PDEs and climate models. By learning a drift over a stochastic interpolation between successive states, the approach achieves efficient sampling and favorable balance across deterministic accuracy, spectral fidelity, and probabilistic calibration. The authors benchmark SI against multiple diffusion and latent-space baselines on Kolmogorov Flow, Rayleigh–Bénard Convection, and PlaSim climate data, showing competitive performance with as few as 2–5 sampling steps in some settings and robust long-horizon spectra in climate emulation. Overall, stochastic interpolants emerge as a strong, flexible baseline for physical emulation with tunable trade-offs and clear guidance for future improvements in turbulent regimes and extended forecasts.

Abstract

Generative models have recently emerged as powerful surrogates for physical systems, demonstrating increased accuracy, stability, and/or statistical fidelity. Most approaches rely on iteratively denoising a Gaussian, a choice that may not be the most effective for autoregressive prediction tasks in PDEs and dynamical systems such as climate. In this work, we benchmark generative models across diverse physical domains and tasks, and highlight the role of stochastic interpolants. By directly learning a stochastic process between current and future states, stochastic interpolants can leverage the proximity of successive physical distributions. This allows for generative models that can use fewer sampling steps and produce more accurate predictions than models relying on transporting Gaussian noise. Our experiments suggest that generative models need to balance deterministic accuracy, spectral consistency, and probabilistic calibration, and that stochastic interpolants can potentially fulfill these requirements by adjusting their sampling. This study establishes stochastic interpolants as a competitive baseline for physical emulation and gives insight into the abilities of different generative modeling frameworks.

Figures (12)

• Figure 1: Left: Typical generative models rely on transporting Gaussian noise $z$, conditioned on a current state $u(t)$. Right: Learning a stochastic process to transport current to future states can be more efficient and accurate. The mixing of the source and target distributions can be controlled by the amount of added noise. $T$ denotes time along a stochastic process, while $t$ is the physical time.
• Figure 2: Distance heuristics for the Rayleigh-Bénard dataset. Distances between samples drawn from successive timesteps $D(u(t), u(t+1))$ and between Gaussian noise and future timesteps $D(N(0, I), u(t+1))$ are plotted for the buoyancy field. Each metric is averaged over a 5-fold cross validation, with the standard deviation shaded.
• Figure 3: CRPS and SSR plots for the considered generative models over 30 days.
• Figure 4: Global surface temperature and precipitation averaged for every 6 months over 100 years.
• Figure 5: VRMSE/SRMSE for model predictions over time on the Kolmogorov Flow (KF) dataset. Each model is trained with three seeds, mean errors are plotted with standard deviations shaded.