Problem
Research questions and friction points this paper is trying to address.
generative denoising models
Jacobian spectrum
diffusion models
flow-matching
spectral properties
On the spectral properties of generative denoiser Jacobians
🤖 AI Summary
This study addresses the limitation of existing evaluation metrics in revealing the underlying mechanistic differences among generative denoising models. To this end, it proposes the Jacobian spectrum as a key analytical tool for distinguishing such models and establishes a novel training paradigm that directly modulates spectral properties. Specifically, by introducing a spectral regularization method based on perturbed inputs, the approach optimizes responses along data-dependent principal directions while suppressing noise-oriented components. Experiments conducted on ImageNet with both diffusion and flow matching models demonstrate that the proposed method effectively enhances the representation of data-dependent features, leading to substantial improvements in image generation quality.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Jacobian spectrum
generative denoiser
spectral regularization
diffusion models
eigenvalue perturbation
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