Discrete generative diffusion models without stochastic differential equations: a tensor network approach

• URL: http://arxiv.org/abs/2407.11133v1
• Date: Mon, 15 Jul 2024 18:00:11 GMT
• Title: Discrete generative diffusion models without stochastic differential equations: a tensor network approach
• Authors: Luke Causer, Grant M. Rotskoff, Juan P. Garrahan,
• Abstract summary: Diffusion models (DMs) are a class of generative machine learning methods. We show how to use networks (TNs) to efficiently define and sample such discrete models''
• Score: 1.5839621757142595
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a ``score function'' that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such ``discrete diffusion models'' (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the $d=1$ constrained Fredkin chain and the $d=2$ Ising model.

Related papers

• 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)
• Glauber Generative Model: Discrete Diffusion Models via Binary Classification [21.816933208895843]
  We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models. GGM deploys a Markov chain to denoise a sequence of noisy tokens to a sample from a joint distribution of discrete tokens. We show that it outperforms existing discrete diffusion models in language generation and image generation.
  arXiv  Detail & Related papers  (2024-05-27T10:42:13Z)
• 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)
• Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization [17.535229185525353]
  We introduce an algorithm leveraging the uniformization of continuous Markov chains, implementing transitions on random time points. Our results align with state-of-the-art achievements for diffusion models in $mathbbRd$ and further underscore the advantages of discrete diffusion models in comparison to the $mathbbRd$ setting.
  arXiv  Detail & Related papers  (2024-02-12T22:26:52Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• 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)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• 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)
• Discrete Denoising Flows [87.44537620217673]
  We introduce a new discrete flow-based model for categorical random variables: Discrete Denoising Flows (DDFs) In contrast with other discrete flow-based models, our model can be locally trained without introducing gradient bias. We show that DDFs outperform Discrete Flows on modeling a toy example, binary MNIST and Cityscapes segmentation maps, measured in log-likelihood.
  arXiv  Detail & Related papers  (2021-07-24T14:47:22Z)
• Variational Mixture of Normalizing Flows [0.0]
  Deep generative models, such as generative adversarial networks autociteGAN, variational autoencoders autocitevaepaper, and their variants, have seen wide adoption for the task of modelling complex data distributions. Normalizing flows have overcome this limitation by leveraging the change-of-suchs formula for probability density functions. The present work overcomes this by using normalizing flows as components in a mixture model and devising an end-to-end training procedure for such a model.
  arXiv  Detail & Related papers  (2020-09-01T17:20:08Z)

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.