Improved Sample Complexity Bounds for Diffusion Model Training

• URL: http://arxiv.org/abs/2311.13745v3
• Date: Mon, 09 Dec 2024 11:50:26 GMT
• Title: Improved Sample Complexity Bounds for Diffusion Model Training
• Authors: Shivam Gupta, Aditya Parulekar, Eric Price, Zhiyang Xun,
• Abstract summary: We show an emphexponential improvement in the dependence onlinear error and depth, along with other relevant parameters.<n>We show an emphexponential improvement in the dependence onlinear error and depth, along with improved dependencies on other relevant parameters.
• Score: 6.20468094368214
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works~\cite{chen2022,chen2022improved,benton2023linear} have studied the iteration complexity of sampling, assuming access to an accurate diffusion model. In this work, we focus on understanding the \emph{sample complexity} of training such a model; how many samples are needed to learn an accurate diffusion model using a sufficiently expressive neural network? Prior work~\cite{BMR20} showed bounds polynomial in the dimension, desired Total Variation error, and Wasserstein error. We show an \emph{exponential improvement} in the dependence on Wasserstein error and depth, along with improved dependencies on other relevant parameters.

Related papers

• Generative Modeling with Bayesian Sample Inference [50.07758840675341]
  We derive a novel generative model from the simple act of Gaussian posterior inference. Treating the generated sample as an unknown variable to infer lets us formulate the sampling process in the language of Bayesian probability. Our model uses a sequence of prediction and posterior update steps to narrow down the unknown sample from a broad initial belief.
  arXiv  Detail & Related papers  (2025-02-11T14:27:10Z)
• Ablation Based Counterfactuals [7.481286710933861]
  Ablation Based Counterfactuals (ABC) is a method of performing counterfactual analysis that relies on model ablation rather than model retraining. We demonstrate how we can construct a model like this using an ensemble of diffusion models. We then use this model to study the limits of training data attribution by enumerating full counterfactual landscapes.
  arXiv  Detail & Related papers  (2024-06-12T06:22:51Z)
• 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)
• Amortizing intractable inference in diffusion models for vision, language, and control [89.65631572949702]
  This paper studies amortized sampling of the posterior over data, $mathbfxsim prm post(mathbfx)propto p(mathbfx)r(mathbfx)$, in a model that consists of a diffusion generative model prior $p(mathbfx)$ and a black-box constraint or function $r(mathbfx)$. We prove the correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from
  arXiv  Detail & Related papers  (2024-05-31T16:18:46Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• Deep adaptive sampling for surrogate modeling without labeled data [4.047684532081032]
  We present a deep adaptive sampling method for surrogate modeling ($textDAS2$) In the parametric setting, the residual loss function can be regarded as an unnormalized probability density function. New samples match the residual-induced distribution, the refined training set can further reduce the statistical error.
  arXiv  Detail & Related papers  (2024-02-17T13:44:02Z)
• Diffusion Random Feature Model [0.0]
  We present a diffusion model-inspired deep random feature model that is interpretable. We derive generalization bounds between the distribution of sampled data and the true distribution using properties of score matching. We validate our findings by generating samples on the fashion MNIST dataset and instrumental audio data.
  arXiv  Detail & Related papers  (2023-10-06T17:59:05Z)
• Hierarchical Integration Diffusion Model for Realistic Image Deblurring [71.76410266003917]
  Diffusion models (DMs) have been introduced in image deblurring and exhibited promising performance. We propose the Hierarchical Integration Diffusion Model (HI-Diff), for realistic image deblurring. Experiments on synthetic and real-world blur datasets demonstrate that our HI-Diff outperforms state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-05-22T12:18:20Z)
• 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)
• Can Push-forward Generative Models Fit Multimodal Distributions? [3.8615905456206256]
  We show that the Lipschitz constant of generative networks has to be large in order to fit multimodal distributions. We validate our findings on one-dimensional and image datasets and empirically show that generative models consisting of stacked networks with input at each step do not suffer of such limitations.
  arXiv  Detail & Related papers  (2022-06-29T09:03:30Z)
• Diffusion models as plug-and-play priors [98.16404662526101]
  We consider the problem of inferring high-dimensional data $mathbfx$ in a model that consists of a prior $p(mathbfx)$ and an auxiliary constraint $c(mathbfx,mathbfy)$. The structure of diffusion models allows us to perform approximate inference by iterating differentiation through the fixed denoising network enriched with different amounts of noise.
  arXiv  Detail & Related papers  (2022-06-17T21:11:36Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)

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.