Capturing Uncertainty in Regression via Conditional Diffusion Models

Qijie Zhu, Oscar Depp, Minshuo Chen, Han Liu

Keywords: uncertainty quantification, regression, diffusion models

Abstract: Quantifying uncertainty is a fundamental problem in both statistics and machine learning. Existing uncertainty quantification (UQ) approaches often suffer from significant limitations, including high computational cost, restrictive parametric assumptions, and overly conservative prediction intervals. In this paper, we propose a UQ framework based on diffusion models. In regression tasks, we learn the full conditional distribution of the response variable given the input features. Our method enables flexible, nonparametric modeling of complex conditional data distributions. We construct prediction intervals from the learned conditional distribution and establish theoretical guarantees on their coverage probabilities. Empirically, we conduct experiments on both synthetic and real-world regression tasks to evaluate the effectiveness of our approach. The results demonstrate that our method achieves competitive or superior performance in predictive uncertainty estimation compared to a range of established baselines, offering a powerful, efficient and theoretically grounded alternative for uncertainty quantification.

Primary Area: generative models

Submission Number: 14650