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arXiv Statistics ML

Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions

The paper introduces Latent Nonlinear Denoising Score Matching (LNDSM), a method that integrates nonlinear, structure-informed latent diffusions with a variational autoencoder framework. LNDSM designs the forward diffusion to admit a chosen reference distribution, such as a Gaussian mixture, and derives a computable approximation to a cross‑entropy upper bound using Euler‑Maruyama discretization. Experiments on benchmark image datasets show that LNDSM improves sample quality, mode balance, and training efficiency compared to conventional latent score‑based generative models.

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arXiv Machine Learning
Aug 26

Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime

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
diffusion
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Hugging Face Trending Papers
Jun 29

Simplifying Flow Matching Transformations with Low-Rank Mixture Models

Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density. However, this choice of latent density can impose unnecessary complexity on the learned flow transformation due to the topological mismatch between the latent and data densities, leading to slower training and suboptimal performance.

diffusion
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arXiv Machine Learning
Oct 12

Transformer-based In-Context Score Operator Learning for Diffusion Models

The paper introduces a transformer-based framework that learns an in‑context score operator for diffusion models, allowing the model to perform reverse‑diffusion sampling on unseen target distributions specified by a small empirical context set. By representing the task‑dependent score as a Gaussian‑kernel conditional mean and approximating it with a transformer‑based query‑dependent attention architecture, the method can adapt to new tasks without retraining or parameter updates. The authors provide theoretical generalization‑error bounds and evaluate the approach on scientific and visual datasets, noting strong performance on simple task families and limitations as task complexity grows.

By Wuzhe Xu, Zhaiming Shen, Yulong Lu, Wenjing Liao, Rongjie Lai
llmsdiffusion
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