Neural diffusion processes provide a scalable, non-Gaussian approach to modelling distributions over functions, but existing formulations are limited to single-task inference and do not capture dependencies across related tasks. In many multi-task regression settings, jointly modelling correlated functions and enabling task-aware conditioning is crucial for improving predictive performance and uncertainty calibration, particularly in low-data regimes. We propose multi-task neural diffusion processes, an extension that incorporates a task encoder to enable task-conditioned probabilistic regression and few-shot adaptation across related functions. The task encoder extracts a low-dimensional representation from context observations and conditions the diffusion model on this representation, allowing information sharing across tasks while preserving input-size agnosticity and the equivariance properties of neural diffusion processes. The resulting framework retains the expressiveness and scalability of neural diffusion processes while enabling efficient transfer to unseen tasks. Empirical results demonstrate improved point prediction accuracy and better-calibrated predictive uncertainty compared to single-task neural diffusion processes and Gaussian process baselines. We validate the approach on real wind farm data appropriate for wind power prediction. In this high-impact application, reliable uncertainty quantification directly supports operational decision-making in wind farm management, illustrating effective few-shot adaptation in a challenging real-world multi-task regression setting.

翻译：神经扩散过程为函数分布建模提供了一种可扩展的非高斯方法，但现有公式仅限于单任务推断，未能捕捉相关任务间的依赖关系。在许多多任务回归场景中，联合建模相关函数并实现任务感知的条件化对于提升预测性能及不确定性校准至关重要，尤其在低数据条件下。本文提出多任务神经扩散过程，该扩展方法通过引入任务编码器实现任务条件化概率回归及相关函数间的少样本适应。任务编码器从上下文观测中提取低维表征，并以此表征为扩散模型提供条件，从而在保持输入尺寸无关性与神经扩散过程等变性特质的同时，实现跨任务信息共享。该框架在保留神经扩散过程表达能力与可扩展性的同时，支持对未见任务的高效迁移。实证结果表明，相较于单任务神经扩散过程与高斯过程基线方法，本方法在点预测精度与预测不确定性校准方面均有提升。我们在适用于风电功率预测的真实风电场数据上验证了该方法的有效性。在这一高影响力应用中，可靠的不确定性量化直接支撑风电场运营管理中的决策制定，展现了该方法在具有挑战性的现实多任务回归场景中实现有效少样本适应的能力。