Master's Thesis Defense: Diffusion-based Conditional Density Estimation for Time Series

Diffusion models have recently achieved significant success across a wide range of applications, including high-fidelity image processing and synthetic data generation. In this work, we propose a new diffusion-based algorithm specifically designed for time series forecasting. Accurate forecasting is fundamental to decision-making in diverse fields such as finance, energy, and meteorology. Inspired by the Lasso regularization method, we integrate the sparsity-inducing principles of Lasso with the diffusion framework to enhance conditional density estimation. Our approach incorporates a "feeding penalty" into the score-matching objective, enabling the model to autonomously identify significant historical lags while filtering out redundant noise. Experimental results demonstrate that our method exhibits superior performance in terms of both predictive accuracy and robustness. By combining the probabilistic flexibility of diffusion models with the feature selection capability of Lasso, this work provides a reliable and interpretable solution for complex forecasting challenges.

Thesis Advisor: Likai Chen