Compare Stochastic Interpolant loss parameterisations

Compare training the Denoising Stochastic Interpolant in terminal-state space with training it in drift space and noise space, determining the relative behavior and performance of these equivalent loss parameterisations for generative weather forecasting.

Background

The paper introduces Denoising Stochastic Interpolants (DSI), in which the neural network predicts the terminal atmospheric state rather than the stochastic-interpolant drift or Wiener noise. The authors derive algebraic equivalences between the terminal-state loss and reweighted drift-space and noise-space losses.

Only the terminal-state formulation is used for training Xaurora. The relative empirical and practical behavior of the three equivalent parameterisations is therefore left unresolved, particularly regarding stability, optimization, and forecasting performance.

References

Note that we train in $x_1$-space and leave the comparison for future work.

— Xaurora: Generative Weather Forecasting with Denoising Stochastic Interpolants from a Foundation Model Prior  (2610.06509 - Walt et al., 5 Oct 2026) in Appendix, Section Methodological details, subsection “Drift parameterisations,” subsubsection “Loss function equivalences”