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.
By Hugo Latourelle-Vigeant, Sinho Chewi, Aram-Alexandre Pooladian, John Sous, Theodor Misiakiewicz
WaveletDiff is a diffusion-based framework that generates time series by training directly on wavelet coefficients, leveraging multi-resolution structure through level‑specific transformers and cross‑level attention with adaptive gating. The model incorporates Parseval‑theorem‑based energy constraints to preserve time‑frequency properties during diffusion. Experiments on six real‑world datasets from energy, finance, and neuroscience show that WaveletDiff outperforms several diffusion baselines and competes with the VAE/transformer‑based MSDformer, achieving lower discriminative and Context‑FID scores while using fewer parameters and less training time.
By Yu-Hsiang Wang, Olgica Milenkovic
arXiv:2509. 24710v2 Announce Type: replace-cross Abstract: Score-based diffusion models are a highly effective method for generating samples from a distribution of images.
By Dennis Elbr\"achter, Giovanni S. Alberti, Matteo Santacesaria
arXiv:2606. 19894v1 Announce Type: new Abstract: The remarkable success of score-based diffusion models has spurred significant efforts to establish their theoretical foundations.
By Xinhe Mu, Zaijiu Shang, Zhaoqi Zhou, Chuan Zhou, Qi Meng, Guiying Yan, Zhiming Ma
arXiv:2502. 19499v4 Announce Type: replace Abstract: Diffusion models have achieved remarkable progress in various domains with an intriguing ability to produce new data that do not exist in the training set.
By Zhengdao Chen
arXiv:2609.30988v1 Announce Type: new
Abstract: Real-world image super-resolution (SR) requires recovering perceptually realistic high-resolution images from complex low-resolution observations while...
By Xin Di, Mingyu Shi, Yuanfei Bao, Long Peng, Yue Zhao, Jiaming Guo, Renjing Pei, Xueyang Fu, Yang Cao, Zheng-Jun Zha
The paper explores using denoising diffusion generative models as plug‑and‑play priors for high‑dimensional inference problems. By combining a pre‑trained diffusion prior with a differentiable auxiliary constraint, the authors enable approximate inference through iterative differentiation across multiple noisy versions of the data. This framework opens possibilities for conditional generation, image segmentation, and novel combinatorial optimization algorithms.
By Alexandros Graikos, Esmeralda S. Whitammer, Nebojsa Jojic, Dimitris Samaras
arXiv:2607. 19332v1 Announce Type: new Abstract: Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching.
By Chirag Vashist, Ke Li
arXiv:2510. 22899v2 Announce Type: replace Abstract: We investigate the role of network architecture in shaping the inductive biases of modern score-based generative models.
By Andreas Floros, Seyed-Mohsen Moosavi-Dezfooli, Pier Luigi Dragotti
arXiv:2606. 00094v1 Announce Type: cross Abstract: Image generative models aim to sample data points from the underlying data manifold, a task that requires learning and decoding a dense, low-dimensional, and compact parameterization space.
By Duoduo Xue, Zhiyu Zhu, Junhui Hou
The paper investigates memorization in diffusion models, showing that the empirical score function is a weighted sum of Gaussian score functions with sharp softmax weights, causing individual training samples to dominate and lead to sampling collapse. By approximating this function with a neural network, the authors obtain a smoother representation that generalizes better. They introduce two techniques—Noise Unconditioning and Temperature Smoothing—to further reduce single‑sample dominance, and demonstrate improved generalization across multiple datasets while preserving generation quality.
By Xinyu Zhou, Jiawei Zhang, Stephen J. Wright
arXiv:2512. 20963v3 Announce Type: replace Abstract: Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective.
By Zekai Zhang, Xiao Li, Xiang Li, Lianghe Shi, Meng Wu, Molei Tao, Qing Qu