The diffusion model has shown remarkable performance in modeling data distributions and synthesizing data. However, the vanilla diffusion model requires complete or fully observed data for training. Incomplete data is a common issue in various real-world applications, including healthcare and finance, particularly when dealing with tabular datasets. This work presents a unified and principled diffusion-based framework for learning from data with missing values under various missing mechanisms. We first observe that the widely adopted "impute-then-generate" pipeline may lead to a biased learning objective. Then we propose to mask the regression loss of Denoising Score Matching in the training phase. We prove the proposed method is consistent in learning the score of data distributions, and the proposed training objective serves as an upper bound for the negative likelihood in certain cases. The proposed framework is evaluated on multiple tabular datasets using realistic and efficacious metrics and is demonstrated to outperform state-of-the-art diffusion model on tabular data with "impute-then-generate" pipeline by a large margin.

翻译：扩散模型在数据分布建模与合成数据生成方面表现卓越。然而，标准扩散模型需要完整观测数据才能进行训练。在实际应用场景中（如医疗健康与金融领域），尤其是处理表格数据集时，数据缺失是常见问题。本文提出统一且具有理论基础的可扩散框架，支持在多种缺失机制下从含缺失值数据中学习。我们首先观察到广泛采用的"插补-生成"流水线可能导致有偏的学习目标，随后提出在训练阶段对去噪分数匹配的回归损失进行掩码处理。我们证明了该方法能一致地学习数据分布的分数函数，并证明该训练目标在特定情况下可作为负似然的上界。该框架采用真实且有效指标在多个表格数据集上评估，结果表明其性能显著优于采用"插补-生成"流水线的先进表格数据扩散模型。