Information Spreading in Diffusion Models from Effective Field Theory

• URL: http://arxiv.org/abs/2608.14308v1
• Date: Fri, 14 Aug 2026 13:45:31 GMT
• Title: Information Spreading in Diffusion Models from Effective Field Theory
• Abstract summary: We study score-matching diffusion models with a convolutional architecture.<n>We argue that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.

Related papers

• Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access [47.96419637803502]
  We present a principled theoretical framework analyzing diffusion models, providing a state-of-the-art sample complexity bound to $widetildemathcalO(epsilon-4)$.<n>Our structured decomposition of the score estimation error into statistical and optimization components offers critical insights into how diffusion models can be trained efficiently.
  arXiv  Detail & Related papers  (2025-05-23T20:02:15Z)
• Can Diffusion Models Disentangle? A Theoretical Perspective [37.21661224725838]
  This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations.<n>We establish identifiability conditions for general disentangled latent variable models, analyze training dynamics, and derive sample complexity bounds for disentangled latent subspace models.
  arXiv  Detail & Related papers  (2025-03-31T20:46:18Z)
• Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling [29.612011138019255]
  We study the emergence of unimodal representation dynamics in diffusion models.<n>The unimodality arises from an interplay between denoising strength and class confidence across noise scales.<n>In classification tasks, the presence of unimodal dynamics reliably reflects the generalization of the diffusion model.
  arXiv  Detail & Related papers  (2025-02-09T01:58:28Z)
• Transformers from Diffusion: A Unified Framework for Neural Message Passing [79.9193447649011]
  Message passing neural networks (MPNNs) have become a de facto class of model solutions.<n>We propose an energy-constrained diffusion model, which integrates the inductive bias of diffusion with layer-wise constraints of energy.<n>Building on these insights, we devise a new class of message passing models, dubbed Transformers (DIFFormer), whose global attention layers are derived from the principled energy-constrained diffusion framework.
  arXiv  Detail & Related papers  (2024-09-13T17:54:41Z)
• Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory [87.00653989457834]
  Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. Despite the empirical success, theory of conditional diffusion models is largely missing. This paper bridges the gap by presenting a sharp statistical theory of distribution estimation using conditional diffusion models.
  arXiv  Detail & Related papers  (2024-03-18T17:08:24Z)
• Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models [59.331993845831946]
  Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. This paper provides the first theoretical study towards understanding the influence of guidance on diffusion models in the context of Gaussian mixture models.
  arXiv  Detail & Related papers  (2024-03-03T23:15:48Z)
• GenEFT: Understanding Statics and Dynamics of Model Generalization via Effective Theory [15.01642959193149]
  We present an effective theory framework for shedding light on the statics and dynamics of neural network generalization.<n>We find generalization in a Goldilocks zone where the decoder is neither too weak nor too powerful.<n>We then introduce an effective theory for the dynamics of representation learning, where latent-space representations are modeled as interacting particles (repons)
  arXiv  Detail & Related papers  (2024-02-08T18:51:55Z)
• Generative Diffusion Models for Lattice Field Theory [8.116039964888353]
  This study delves into the connection between machine learning and lattice field theory by linking generative diffusion models (DMs) with quantization. We show that DMs can be conceptualized by reversing a process driven by the Langevin equation, which then produces samples from an initial distribution to approximate the target distribution.
  arXiv  Detail & Related papers  (2023-11-06T22:24:28Z)
• SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases [66.61789780666727]
  We show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property. We also offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states. Our model yields a significant improvement over the state-of-the-art baselines.
  arXiv  Detail & Related papers  (2023-08-25T07:15:58Z)
• Diffusion Models are Minimax Optimal Distribution Estimators [49.47503258639454]
  We provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling. We show that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates.
  arXiv  Detail & Related papers  (2023-03-03T11:31:55Z)
• How Much is Enough? A Study on Diffusion Times in Score-based Generative Models [76.76860707897413]
  Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution. We show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process.
  arXiv  Detail & Related papers  (2022-06-10T15:09:46Z)
• Flow-based sampling for fermionic lattice field theories [8.46509435333566]
  This work develops approaches that enable flow-based sampling of theories with dynamical fermions. As a practical demonstration, these methods are applied to the sampling of field configurations for a two-dimensional theory of massless staggered fermions.
  arXiv  Detail & Related papers  (2021-06-10T17:32:47Z)
• Breakdown signatures of the phenomenological Lindblad master equation in the strong optomechanical coupling regime [0.0]
  The Lindblad form of the master equation has proven to be one of the most convenient ways to describe an environment interacting with a quantum system of interest. We investigate the differences between a common phenomenological model for the master equation and the more rigorous dressed-state master equation for optomechanical systems. Our work is a step forward toward a better understanding of the role of the coupling between subsystems for open-quantum-system dynamics.
  arXiv  Detail & Related papers  (2020-07-06T23:00:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.