CNL-Diff: A Nonlinear Data Transformation Framework for Epidemic Scale Prediction Based on Diffusion Models

In recent years, the complexity and suddenness of infectious disease transmission have posed significant limitations for traditional time-series forecasting methods when dealing with the nonlinearity, non-stationarity, and multi-peak distributions of epidemic scale variations. To address this challenge, this paper proposes a forecasting framework based on diffusion models, called CNL-Diff, aimed at tackling the prediction challenges in complex dynamics, nonlinearity, and non-stationary distributions. Traditional epidemic forecasting models often rely on fixed linear assumptions, which limit their ability to accurately predict the incidence scale of infectious diseases. The CNL-Diff framework integrates a forward–backward consistent conditioning mechanism and nonlinear data transformations, enabling it to capture the intricate temporal and feature dependencies inherent in epidemic data. The results show that this method outperforms baseline models in metrics such as Mean Absolute Error (MAE), Continuous Ranked Probability Score (CRPS), and Prediction Interval Coverage Probability (PICP). This study demonstrates the potential of diffusion models in complex-distribution time-series modeling, providing a more reliable probabilistic forecasting tool for public health monitoring, epidemic early warning, and risk decision making.