# Forced-Dissipative Stochastic Interpolants

Partially observed dynamical systems expose only coarse-grained slow variables, while unresolved fast variables enter as random effects, so data-driven climate emulators must be probabilistic, yet generative models such as diffusion models lack stability guarantees over long autoregressive rollouts. Forced-dissipative stochastic interpolants write the energy injection and dissipation structure of turbulence into the drift network as a hard constraint, and a Foster–Lyapunov drift condition for the Markov chain proves geometric ergodicity of the emulator. On the two-scale Lorenz-96 prototype, the emulator stays stable over long integrations and under finite-amplitude external forcing, and accurately predicts the forced response of both mean and variance.

Partially observed dynamical systems expose only coarse-grained slow variables, while unresolved fast variables enter as random effects, so data-driven climate emulators must be probabilistic, yet generative models such as diffusion models lack stability guarantees over long autoregressive rollouts. Forced-dissipative stochastic interpolants write the energy injection and dissipation structure of turbulence into the drift network as a hard constraint, and a Foster–Lyapunov drift condition for the Markov chain proves geometric ergodicity of the emulator. On the two-scale Lorenz-96 prototype, the emulator stays stable over long integrations and under finite-amplitude external forcing, and accurately predicts the forced response of both mean and variance.