On the spectral properties of generative denoiser Jacobians
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The paper investigates training objectives for denoising-based generative models, focusing on loss weighting and output parameterization such as noise-, clean image-, and velocity-based formulations. It conducts a systematic numerical study across synthetic datasets with controlled geometry and real image data, evaluating denoising accuracy via PSNR and generative quality via FID. The goal is to disentangle how training choices interact with data manifold dimensionality, model architecture, and dataset size, offering practical design insights rather than proposing a new method.
The paper proposes a deep learning framework that learns priors for inverse problems by exploiting the relationship between proximal operators and Hamilton–Jacobi partial differential equations. Unlike existing methods that require inverting the prior after training, this approach learns the prior directly, enabling efficient evaluation in a single forward pass. Numerical experiments demonstrate the method’s effectiveness in dimensions up to 64.
The paper investigates diffusion models trained in a lazy high‑dimensional regime, extending benign overfitting theory to generative settings. By analyzing denoising score matching in a vector‑valued RKHS with an inner‑product kernel, the authors derive exact risk trajectories under gradient flow when the number of samples scales proportionally with dimensionality. These trajectories reveal three distinct phases—spectral generalization, noise‑dominated interpolation, and empirical Bayes memorization—whose interplay shapes the distribution of generated samples.
arXiv:2606. 04299v1 Announce Type: cross Abstract: We consider the problem of generating images whose internal structure -- defined by the distribution of patches across multiple scales -- matches that of a single reference image.
arXiv:2607. 19332v1 Announce Type: new Abstract: Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching.
arXiv:2607. 17673v1 Announce Type: cross Abstract: Contrastive learning is increasingly moving toward settings with three or more modalities instead of image-text pairs.