用扩散模型学习预测分布，提升回归不确定性量化能力。
Improved probabilistic regression using diffusion models
- 非参数化建模扩散噪声分布，适应多种回归任务。
- 在多维和低维任务中均优于现有基线，且不确定性校准良好。
- 适合需要准确不确定性估计的科研与工业场景。
概率回归通过建模响应变量的完整预测分布，提供比传统点估计更丰富的信息，并直接支持不确定性量化。尽管基于扩散的生成模型在复杂高维数据生成方面表现卓越，但其在一般回归任务中的应用仍缺乏与不确定性相关的评估，且多局限于特定领域。本文提出一种新的基于扩散的概率回归框架，以非参数方式学习预测分布。具体而言，我们建模扩散噪声的完整分布，从而适应多样任务并增强不确定性量化。研究了不同噪声参数化方案，分析其权衡关系，并在涵盖低维与高维设置的广泛回归任务上评估该框架。多个实验表明，该方法在性能上超越现有基线，同时提供校准良好的不确定性估计，展示了其作为概率预测工具的通用性。
原文摘要 · Abstract (English)
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models have shown remarkable success in generating complex, high-dimensional data, their usage in general regression tasks often lacks uncertainty-related evaluation and remains limited to domain-specific applications. We propose a novel diffusion-based framework for probabilistic regression that learns predictive distributions in a nonparametric way. More specifically, we propose to model the full distribution of the diffusion noise, enabling adaptation to diverse tasks and enhanced uncertainty quantification. We investigate different noise parameterizations, analyze their trade-offs, and evaluate our framework across a broad range of regression tasks, covering low- and high-dimensional settings. For several experiments, our approach shows superior performance against existing baselines, while delivering calibrated uncertainty estimates, demonstrating its versatility as a tool for probabilistic prediction.
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