发表机构
Stony Brook University; Microsoft Research（石溪大学; 微软研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出用去噪器雅可比矩阵的谱性质刻画生成式去噪模型差异，发现谱特征值与生成性能相关，并引入正则化方法在ImageNet上验证了谱调整可提升生成质量。
AI 中文摘要
生成式去噪模型，如扩散模型和流匹配模型，通过训练深度神经网络去噪器从噪声污染的样本中恢复干净数据，从而学习从复杂分布中采样。虽然这类模型通常根据其合成样本的质量进行比较，但这些指标对于驱动生成过程的底层去噪器之间的差异所提供的洞察有限。在本工作中，我们提出分析去噪器雅可比矩阵的谱，以此作为刻画这些差异的工具。在多个预训练去噪模型中，我们观察到更好的生成性能与更大的雅可比矩阵特征值相关联。受此启发，我们引入了一种正则化方案，通过在扰动输入上训练去噪器来控制雅可比矩阵的谱，其中扰动抑制或放大雅可比矩阵的响应。在ImageNet上，我们测试了直接修改雅可比矩阵谱性质是否能带来更好的生成结果。我们的发现表明，去噪器既受益于增强沿数据相关主特征方向上的响应，也受益于抑制噪声的、与数据无关的响应。这确立了去噪器雅可比矩阵作为识别生成式去噪模型之间差异的有用工具。
英文摘要
Generative denoising models, such as diffusion and flow-matching, learn to sample from complex distributions by training a deep neural network denoiser to recover clean data from noise-corrupted samples. While such models are typically compared on the quality of their synthesized samples, these metrics provide limited insight into how the underlying denoiser, which drives generation, differs. In this work, we propose to analyze the spectrum of the denoiser Jacobian as a tool to characterize these differences. Across pre-trained denoising models, we observe that better generative performance is associated with larger Jacobian eigenvalues. Motivated by this, we introduce a regularization scheme that controls the Jacobian spectrum by training the denoiser on perturbed inputs, with perturbations suppressing or amplifying Jacobian responses. On ImageNet, we test whether directly modifying the Jacobian spectral properties leads to improved generations. Our findings suggest that denoisers benefit from both strengthening responses along data-relevant principal eigen-directions and suppressing the noisy, data-irrelevant ones. This establishes the denoiser Jacobian as a useful tool for identifying differences between generative denoising models.
