# Spatiotemporal Prediction

Diffusion models for spatiotemporal prediction usually add independent noise to each future frame and leave temporal dependence to the denoiser. DSSD instead builds the temporal operator of the corruption process from a learnable diagonal state-space model whose decay rates and frequencies train jointly with the denoiser, and uses the Cholesky factor of that model's stationary covariance so the operator stays causal, exactly invertible and unit-variance per frame. On SEVIR, Turbulence, BAIR and RoboNet it beats diffusion baselines sharing the same denoiser, with raw CRPS 3.975 versus 4.174 for the strongest SEVIR baseline, DPM.

Diffusion models for spatiotemporal prediction usually add independent noise to each future frame and leave temporal dependence to the denoiser. DSSD instead builds the temporal operator of the corruption process from a learnable diagonal state-space model whose decay rates and frequencies train jointly with the denoiser, and uses the Cholesky factor of that model's stationary covariance so the operator stays causal, exactly invertible and unit-variance per frame. On SEVIR, Turbulence, BAIR and RoboNet it beats diffusion baselines sharing the same denoiser, with raw CRPS 3.975 versus 4.174 for the strongest SEVIR baseline, DPM.