Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models

• URL: http://arxiv.org/abs/2411.18702v2
• Date: Mon, 07 Jul 2025 23:20:26 GMT
• Title: Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models
• Authors: Chicago Y. Park, Michael T. McCann, Cristina Garcia-Cardona, Brendt Wohlberg, Ulugbek S. Kamilov,
• Abstract summary: Diffusion models have emerged as powerful tools for generating realistic, synthetic signals.<n>We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results.
• Score: 11.161487364062667
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals -- particularly natural images -- and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.

Related papers

• Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics [7.873510219469276]
  We introduce two novel training methods for discrete diffusion samplers.<n>These methods yield memory-efficient training and achieve state-of-the-art results in unsupervised optimization.<n>We introduce adaptations of SN-NIS and Neural Chain Monte Carlo that enable for the first time the application of discrete diffusion models to this problem.
  arXiv  Detail & Related papers  (2025-02-12T18:59:55Z)
• Accelerated Diffusion Models via Speculative Sampling [89.43940130493233]
  Speculative sampling is a popular technique for accelerating inference in Large Language Models. We extend speculative sampling to diffusion models, which generate samples via continuous, vector-valued Markov chains. We propose various drafting strategies, including a simple and effective approach that does not require training a draft model.
  arXiv  Detail & Related papers  (2025-01-09T16:50:16Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional general score-mismatched diffusion samplers. We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions. This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Distillation of Discrete Diffusion through Dimensional Correlations [21.078500510691747]
  "Mixture" models are capable of treating dimensional correlations while remaining scalable.<n>Loss functions enable the mixture models to distill such many-step conventional models into just a few steps by learning the dimensional correlations.<n>Results show the effectiveness of the proposed method in distilling pretrained discrete diffusion models across image and language domains.
  arXiv  Detail & Related papers  (2024-10-11T10:53:03Z)
• Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding [84.3224556294803]
  Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. We aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Our algorithm integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future.
  arXiv  Detail & Related papers  (2024-08-15T16:47:59Z)
• A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization [7.378582040635655]
  Current deep learning approaches rely on generative models that yield exact sample likelihoods. This work introduces a method that lifts this restriction and opens the possibility to employ highly expressive latent variable models. We experimentally validate our approach in data-free Combinatorial Optimization and demonstrate that our method achieves a new state-of-the-art on a wide range of benchmark problems.
  arXiv  Detail & Related papers  (2024-06-03T17:55:02Z)
• Improved off-policy training of diffusion samplers [93.66433483772055]
  We study the problem of training diffusion models to sample from a distribution with an unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods. Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work.
  arXiv  Detail & Related papers  (2024-02-07T18:51:49Z)
• Renormalizing Diffusion Models [0.7252027234425334]
  We use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Our work provides an interpretation of multiscale diffusion models, and gives physically-inspired suggestions for diffusion models which should have novel properties.
  arXiv  Detail & Related papers  (2023-08-23T18:02:31Z)
• 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)
• Infinite-Dimensional Diffusion Models [4.342241136871849]
  We formulate diffusion-based generative models in infinite dimensions and apply them to the generative modeling of functions. We show that our formulations are well posed in the infinite-dimensional setting and provide dimension-independent distance bounds from the sample to the target measure. We also develop guidelines for the design of infinite-dimensional diffusion models.
  arXiv  Detail & Related papers  (2023-02-20T18:00:38Z)
• Fast Inference in Denoising Diffusion Models via MMD Finetuning [23.779985842891705]
  We present MMD-DDM, a novel method for fast sampling of diffusion models. Our approach is based on the idea of using the Maximum Mean Discrepancy (MMD) to finetune the learned distribution with a given budget of timesteps. Our findings show that the proposed method is able to produce high-quality samples in a fraction of the time required by widely-used diffusion models.
  arXiv  Detail & Related papers  (2023-01-19T09:48:07Z)
• Fast Sampling of Diffusion Models via Operator Learning [74.37531458470086]
  We use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose a parallel decoding method. We show our method achieves state-of-the-art FID of 3.78 for CIFAR-10 and 7.83 for ImageNet-64 in the one-model-evaluation setting.
  arXiv  Detail & Related papers  (2022-11-24T07:30:27Z)
• On Distillation of Guided Diffusion Models [94.95228078141626]
  We propose an approach to distilling classifier-free guided diffusion models into models that are fast to sample from. For standard diffusion models trained on the pixelspace, our approach is able to generate images visually comparable to that of the original model. For diffusion models trained on the latent-space (e.g., Stable Diffusion), our approach is able to generate high-fidelity images using as few as 1 to 4 denoising steps.
  arXiv  Detail & Related papers  (2022-10-06T18:03:56Z)
• 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)
• Deblurring via Stochastic Refinement [85.42730934561101]
  We present an alternative framework for blind deblurring based on conditional diffusion models. Our method is competitive in terms of distortion metrics such as PSNR.
  arXiv  Detail & Related papers  (2021-12-05T04:36:09Z)
• Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
  We take a two-step approach by first modeling the probability distribution and then sampling from that model. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
  arXiv  Detail & Related papers  (2021-10-20T12:25:22Z)

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.