score-based-diffusion

This paper establishes a rigorous quantitative connection between neural network score function approximation and the resulting distribution approximation in score-based diffusion models, proving that accurate score approximation leads to close distribution approximation in KL divergence, with an explicit bound.

This paper proposes using the Ensemble Score Filter (EnSF), a score-based diffusion data assimilation method, to correct forecasts from a pretrained spatio-temporal energy consumption model using noisy partial observations. Numerical experiments show EnSF significantly improves state estimation over open-loop propagation and outperforms the Ensemble Kalman Filter under nonlinear observations.