Clarify the unexplored geometry of non-Gaussian stochastic interpolants

Characterize the geometrical consequences of combining Stochastic Interpolants with non-Gaussian noise models for high-dimensional generative weather forecasting.

Background

The stochastic term in Xaurora’s SDE currently uses Gaussian noise, whose spectral properties contribute substantially to the model’s persistent noise floor. The authors note that Stochastic Interpolants do not technically require Gaussian noise, so alternative noise distributions could be considered.

Although non-Gaussian noise models may offer a route to better-matched forecast spectra and calibration, the geometric implications of replacing Gaussian noise within the Stochastic Interpolant framework are explicitly described as insufficiently understood.

References

Stochastic Interpolants technically do not require the noise to follow a Gaussian distribution. Hence, combining SI with different noise models should be possible, although the geometrical aspect of the problem remains fairly unexplored.

— Xaurora: Generative Weather Forecasting with Denoising Stochastic Interpolants from a Foundation Model Prior  (2610.06509 - Walt et al., 5 Oct 2026) in Section Conclusion, subsection “Limitations and future work”