While achieving remarkable performances, we show that diffusion models are fragile to the presence of noisy samples, limiting their potential in the vast amount of settings where, unlike image synthesis, we are not blessed with clean data. Motivated by our finding that such fragility originates from the distribution gaps between noisy and clean samples along the diffusion process, we introduce risk-sensitive SDE, a stochastic differential equation that is parameterized by the risk (i.e., data "dirtiness") to adjust the distributions of noisy samples, reducing misguidance while benefiting from their contained information. The optimal expression for risk-sensitive SDE depends on the specific noise distribution, and we derive its parameterizations that minimize the misguidance of noisy samples for both Gaussian and general non-Gaussian perturbations. We conduct extensive experiments on both synthetic and real-world datasets (e.g., medical time series), showing that our model effectively recovers the clean data distribution from noisy samples, significantly outperforming conditional generation baselines.

通过引入风险敏感的随机微分方程，我们的研究表明扩散模型在存在噪声样本时非常脆弱，限制了其在诸多设置中的潜力，我们通过调整噪声样本的分布并减少误导性信息，成功地从噪声样本中恢复出干净的数据分布，实验证明我们的模型在合成和真实数据集上明显优于条件生成基准模型。

风险敏感扩散：从噪声采样中学习潜在分布