A Probabilistic Short-Term Load Forecasting with Conditional Diffusion and Split-Conformal Calibration Across Different Aggregation Levels

Probabilistic load forecasting requires reliable uncertainty estimates in addition to point predictions. This paper studies a conditional diffusion forecaster across national, regional, and household demand. The three datasets were preprocessed separately using the same 168-hour lookback, 24-hour horizon, and followed the same calibration pipeline. The diffusion model generated 50 trajectories for each forecast to form 90% prediction intervals. CNN-LSTM and N-BEATSx were used as point
forecasting baselines. N-BEATSx achieved the best point accuracy, while the diffusion model provided predictive distributions that the baselines could not produce. Forecast difficulty increased from 0.037 at the national level to 0.416 at the household level. However, the calibration failure did not follow this pattern.
The raw interval outputs of the diffusion model were under dispersed, with coverage from 0.631 to 0.808, so split conformal calibration was applied to restore the nominal 0.90 level. The split-conformal calibration improved coverage but remained below 0.90 for every dataset, whereas the block-random calibration restored coverage to 0.895–0.905. Panama showed the largest train-to-test mean temporal distribution shift (+0.3910) and the lowest chronological coverage of 0.843. These results
identify the directional temporal drift as a distinct failure mode of conformal calibration in chronologically partitioned load data. These findings are relevant to operational forecasting systems that rely on conformal intervals for reserve planning and risk assessment under non-stationary demand.