Can Diffusion Models Disentangle? A Theoretical Perspective

• URL: http://arxiv.org/abs/2504.00220v1
• Date: Mon, 31 Mar 2025 20:46:18 GMT
• Title: Can Diffusion Models Disentangle? A Theoretical Perspective
• Authors: Liming Wang, Muhammad Jehanzeb Mirza, Yishu Gong, Yuan Gong, Jiaqi Zhang, Brian H. Tracey, Katerina Placek, Marco Vilela, James R. Glass,
• Abstract summary: 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.
• Score: 52.360881354319986
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models, analyze training dynamics, and derive sample complexity bounds for disentangled latent subspace models. To validate our theory, we conduct disentanglement experiments across diverse tasks and modalities, including subspace recovery in latent subspace Gaussian mixture models, image colorization, image denoising, and voice conversion for speech classification. Additionally, our experiments show that training strategies inspired by our theory, such as style guidance regularization, consistently enhance disentanglement performance.

Related papers

• Generalized Diffusion Model with Adjusted Offset Noise [1.7767466724342067]
  We propose a generalized diffusion model that naturally incorporates additional noise within a rigorous probabilistic framework.<n>We derive a loss function based on the evidence lower bound, establishing its theoretical equivalence to offset noise with certain adjustments.<n>Experiments on synthetic datasets demonstrate that our model effectively addresses brightness-related challenges and outperforms conventional methods in high-dimensional scenarios.
  arXiv  Detail & Related papers  (2024-12-04T08:57:03Z)
• On the Feature Learning in Diffusion Models [26.53807235141923]
  We propose a feature learning framework aimed at analyzing and comparing the training dynamics of diffusion models with those of traditional classification models. Our theoretical analysis demonstrates that diffusion models, due to the denoising objective, are encouraged to learn more balanced and comprehensive representations of the data. In contrast, neural networks with a similar architecture trained for classification tend to prioritize learning specific patterns in the data, often focusing on easy-to-learn components.
  arXiv  Detail & Related papers  (2024-12-02T00:41:25Z)
• Latent Abstractions in Generative Diffusion Models [13.344019183402867]
  We study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions. We present a novel theoretical framework that extends NLF, and that offers a unique perspective on SDE-based generative models.
  arXiv  Detail & Related papers  (2024-10-04T12:34:24Z)
• How Diffusion Models Learn to Factorize and Compose [14.161975556325796]
  Diffusion models are capable of generating photo-realistic images that combine elements which likely do not appear together in the training set. We investigate whether and when diffusion models learn semantically meaningful and factorized representations of composable features.
  arXiv  Detail & Related papers  (2024-08-23T17:59:03Z)
• Learning Discrete Concepts in Latent Hierarchical Models [73.01229236386148]
  Learning concepts from natural high-dimensional data holds potential in building human-aligned and interpretable machine learning models.<n>We formalize concepts as discrete latent causal variables that are related via a hierarchical causal model.<n>We substantiate our theoretical claims with synthetic data experiments.
  arXiv  Detail & Related papers  (2024-06-01T18:01:03Z)
• 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)
• Structure Preserving Diffusion Models [19.374406313635966]
  This paper focuses on structure-preserving diffusion models (SPDM)<n>We propose a new framework that considers the geometric structures affecting the diffusion process.<n>We implement an equivariant denoising diffusion bridge model, which achieves reliable equivariant image noise reduction and style transfer.
  arXiv  Detail & Related papers  (2024-02-29T17:16:20Z)
• Diffeomorphic Measure Matching with Kernels for Generative Modeling [1.2058600649065618]
  This article presents a framework for transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs) A theoretical analysis of the proposed method is presented, giving a priori error bounds in terms of the complexity of the model, the number of samples in the training set, and model misspecification.
  arXiv  Detail & Related papers  (2024-02-12T21:44:20Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC [102.64648158034568]
  diffusion models have quickly become the prevailing approach to generative modeling in many domains. We propose an energy-based parameterization of diffusion models which enables the use of new compositional operators. We find these samplers lead to notable improvements in compositional generation across a wide set of problems.
  arXiv  Detail & Related papers  (2023-02-22T18:48:46Z)
• Bi-Noising Diffusion: Towards Conditional Diffusion Models with Generative Restoration Priors [64.24948495708337]
  We introduce a new method that brings predicted samples to the training data manifold using a pretrained unconditional diffusion model. We perform comprehensive experiments to demonstrate the effectiveness of our approach on super-resolution, colorization, turbulence removal, and image-deraining tasks.
  arXiv  Detail & Related papers  (2022-12-14T17:26:35Z)

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.