Scenario generation is a critical component in stochastic programming (SP), as it directly influences the quality of decision-making under uncertainty. Existing approaches predominantly rely on either sampling-based techniques or supervised learning using neural networks. Sampling-based techniques often struggle to capture complex dependencies and rare but plausible events, while supervised learning requires fixed input-output pairs for training and is limited in its ability to generate a wide variety of realistic scenarios that are not restricted by predefined patterns or rules. To address these limitations, we introduce Diff2SP, a diffusion-based generative framework that incorporates downstream optimization objectives directly into scenario generation. Unlike conventional methods that treat scenario generation and decision-making as separate steps, Diff2SP embeds stochastic optimization into the training process, enabling the generation of scenarios that are both statistically coherent and decision-aware. To formally justify this optimization-aware design, we establish a regret bounds that link distributional accuracy to decision quality, and establish sample complexity guarantees showing faster convergence than traditional generative models such as GANs. Empirical results on both synthetic and power-system datasets validate these theoretical insights, demonstrating that Diff2SP consistently improves both statistical fidelity and downstream optimization outcomes.

翻译：场景生成是随机规划（SP）中的关键组成部分，直接影响不确定性下决策的质量。现有方法主要依赖基于采样的技术或使用神经网络的监督学习。基于采样的技术往往难以捕捉复杂依赖关系和罕见但可能发生的事件，而监督学习需要固定的输入-输出对进行训练，且其生成不受预定义模式或规则限制的多样真实场景的能力有限。为克服这些局限性，我们提出Diff2SP——一种基于扩散的生成框架，将下游优化目标直接融入场景生成过程。与将场景生成和决策制定视为独立步骤的传统方法不同，Diff2SP将随机优化嵌入训练过程，从而生成既具有统计连贯性又具备决策感知能力的场景。为从理论上证明这种优化感知设计的合理性，我们建立了将分布精度与决策质量相关联的遗憾界，并给出了样本复杂度保证，表明其收敛速度优于传统生成模型（如GAN）。在合成数据集和电力系统数据集上的实证结果验证了这些理论洞见，表明Diff2SP在统计保真度和下游优化效果上均有一致提升。