提出可快速计算扩散模型对数据扰动的敏感度，无需重训练即可预估样本变化。
Sensitivity Analysis for Diffusion Models
- 基于黑箱得分模型推导出训练映射的导数闭式解
- 计算开销与采样相当，能准确预测微小数据扰动后的样本变化
- 适用于图像扩散模型的快速调试与鲁棒性分析
训练扩散模型本质上是将数据分布 $ρ$ 映射到该分布的最优得分函数 $s_t$。我们能否对此映射求导？若能，则可在不重新训练的情况下，预测数据集的小幅扰动如何影响得分函数及生成样本。本文给出了仅需黑箱访问预训练得分模型及其输入导数的闭式导数计算方法。进一步扩展至估计扩散模型样本对目标测度加性扰动的敏感性，计算时间与采样和路径对数似然计算相当。所提方法对数值误差和近似误差具有鲁棒性，其敏感性结果与图像扩散模型重训练或微调后样本的实际变化高度相关。
原文摘要 · Abstract (English)
Training a diffusion model approximates a map from a data distribution $ρ$ to the optimal score function $s_t$ for that distribution. Can we differentiate this map? If we could, then we could predict how the score, and ultimately the model's samples, would change under small perturbations to the training set before committing to costly retraining. We give a closed-form procedure for computing this map's directional derivatives, relying only on black-box access to a pre-trained score model and its derivatives with respect to its inputs. We extend this result to estimate the sensitivity of a diffusion model's samples to additive perturbations of its target measure, with runtime comparable to sampling from a diffusion model and computing log-likelihoods along the sample path. Our method is robust to numerical and approximation error, and the resulting sensitivities correlate with changes in an image diffusion model's samples after retraining and fine-tuning.
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