MAD: Manifold Attracted Diffusion

• URL: http://arxiv.org/abs/2509.24710v1
• Date: Mon, 29 Sep 2025 12:40:20 GMT
• Title: MAD: Manifold Attracted Diffusion
• Authors: Dennis Elbrächter, Giovanni S. Alberti, Matteo Santacesaria,
• Abstract summary: We introduce the notion of an extended score and show that, in a simplified setting, it can be used to reduce small variations to zero.<n>We describe how its approximation can be computed efficiently from an approximation to the standard score and demonstrate its efficacy on toy problems, synthetic data, and real data.
• Score: 2.3322477552758234
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an efficiently implementable modification of the inference procedure to generate noiseless samples. Our approach is motivated by the manifold hypothesis, according to which meaningful data is concentrated around some low-dimensional manifold of a high-dimensional ambient space. The central idea is that noise manifests as low magnitude variation in off-manifold directions in contrast to the relevant variation of the desired distribution which is mostly confined to on-manifold directions. We introduce the notion of an extended score and show that, in a simplified setting, it can be used to reduce small variations to zero, while leaving large variations mostly unchanged. We describe how its approximation can be computed efficiently from an approximation to the standard score and demonstrate its efficacy on toy problems, synthetic data, and real data.

Related papers

• Stochastic Variational Inference with Tuneable Stochastic Annealing [1.6385815610837167]
  We present a modified variational inference (SVI) approach applicable to both large and small datasets.<n>We are motivated by the fact that, in SVI, the larger the batch size the more approximately Gaussian is the intrinsic noise, but the smaller its variance.<n>We propose a simple method for achieving both goals of having larger variance noise to escape bad local optimal solutions and more data information to obtain more accurate gradient directions.
  arXiv  Detail & Related papers  (2025-04-04T19:46:10Z)
• Diffusing Differentiable Representations [60.72992910766525]
  We introduce a novel, training-free method for sampling differentiable representations (diffreps) using pretrained diffusion models.<n>We identify an implicit constraint on the samples induced by the diffrep and demonstrate that addressing this constraint significantly improves the consistency and detail of the generated objects.
  arXiv  Detail & Related papers  (2024-12-09T20:42:58Z)
• Diffusion Attribution Score: Evaluating Training Data Influence in Diffusion Models [22.39558434131574]
  Existing data attribution methods for diffusion models typically quantify the contribution of a training sample.<n>We argue that the direct usage of diffusion loss cannot represent such a contribution accurately due to the calculation of diffusion loss.<n>We propose Diffusion Attribution Score (textitDAS) to measure the direct comparison between predicted distributions with an attribution score.
  arXiv  Detail & Related papers  (2024-10-24T10:58:17Z)
• Diffusion Priors for Variational Likelihood Estimation and Image Denoising [10.548018200066858]
  We propose adaptive likelihood estimation and MAP inference during the reverse diffusion process to tackle real-world noise. Experiments and analyses on diverse real-world datasets demonstrate the effectiveness of our method.
  arXiv  Detail & Related papers  (2024-10-23T02:52:53Z)
• Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matching [27.2761325416843]
  We leverage the recently proposed covariance moment matching technique and introduce a novel method for learning the diagonal covariance.<n>We demonstrate how our method can substantially enhance the sampling efficiency, recall rate and likelihood of commonly used diffusion models.
  arXiv  Detail & Related papers  (2024-06-16T05:47:12Z)
• 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)
• Semi-Implicit Denoising Diffusion Models (SIDDMs) [50.30163684539586]
  Existing models such as Denoising Diffusion Probabilistic Models (DDPM) deliver high-quality, diverse samples but are slowed by an inherently high number of iterative steps. We introduce a novel approach that tackles the problem by matching implicit and explicit factors. We demonstrate that our proposed method obtains comparable generative performance to diffusion-based models and vastly superior results to models with a small number of sampling steps.
  arXiv  Detail & Related papers  (2023-06-21T18:49:22Z)
• 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)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• 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)
• A Variational Perspective on Diffusion-Based Generative Models and Score Matching [8.93483643820767]
  We derive a variational framework for likelihood estimation for continuous-time generative diffusion. We show that minimizing the score-matching loss is equivalent to maximizing a lower bound of the likelihood of the plug-in reverse SDE.
  arXiv  Detail & Related papers  (2021-06-05T05:50:36Z)

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.