Lecture Notes in Probabilistic Diffusion Models

• URL: http://arxiv.org/abs/2312.10393v1
• Date: Sat, 16 Dec 2023 09:36:54 GMT
• Title: Lecture Notes in Probabilistic Diffusion Models
• Authors: Inga Str\"umke, Helge Langseth
• Abstract summary: Diffusion models are loosely modelled based on non-equilibrium thermodynamics. The diffusion model learns the data manifold to which the original and thus the reconstructed data samples belong. Diffusion models have -- unlike variational autoencoder and flow models -- latent variables with the same dimensionality as the original data.
• Score: 0.5361320134021585
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite similar, namely the process of transforming a complex distribution $p_{\text{complex}}$ on $\mathbb{R}^d$ to a simple distribution $p_{\text{prior}}$ on the same domain. This constitutes a Markov chain of diffusion steps of slowly adding random noise to data, followed by a reverse diffusion process in which the data is reconstructed from the noise. The diffusion model learns the data manifold to which the original and thus the reconstructed data samples belong, by training on a large number of data points. While the diffusion process pushes a data sample off the data manifold, the reverse process finds a trajectory back to the data manifold. Diffusion models have -- unlike variational autoencoder and flow models -- latent variables with the same dimensionality as the original data, and they are currently\footnote{At the time of writing, 2023.} outperforming other approaches -- including Generative Adversarial Networks (GANs) -- to modelling the distribution of, e.g., natural images.

Related papers

• Constrained Diffusion Models via Dual Training [80.03953599062365]
  Diffusion processes are prone to generating samples that reflect biases in a training dataset. We develop constrained diffusion models by imposing diffusion constraints based on desired distributions. We show that our constrained diffusion models generate new data from a mixture data distribution that achieves the optimal trade-off among objective and constraints.
  arXiv  Detail & Related papers  (2024-08-27T14:25:42Z)
• 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)
• 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)
• 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)
• Bayesian Flow Networks [4.585102332532472]
  This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference. Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models. BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.
  arXiv  Detail & Related papers  (2023-08-14T09:56:35Z)
• Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions [22.04182099405728]
  Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this inference diffusion process to generate samples. We show how to maximize a lower-bound on the likelihood for any number of auxiliary variables. We then demonstrate how to parameterize the diffusion for a specified target noise distribution.
  arXiv  Detail & Related papers  (2023-02-14T18:57:04Z)
• Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data [68.62134204367668]
  This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. The generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution.
  arXiv  Detail & Related papers  (2023-02-14T17:02:35Z)
• 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)
• From Points to Functions: Infinite-dimensional Representations in Diffusion Models [23.916417852496608]
  Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution. We show that a combination of information content from different time steps gives a strictly better representation for the downstream task.
  arXiv  Detail & Related papers  (2022-10-25T05:30:53Z)
• Diffusion Models in Vision: A Survey [80.82832715884597]
  A diffusion model is a deep generative model that is based on two stages, a forward diffusion stage and a reverse diffusion stage. Diffusion models are widely appreciated for the quality and diversity of the generated samples, despite their known computational burdens.
  arXiv  Detail & Related papers  (2022-09-10T22:00:30Z)
• Truncated Diffusion Probabilistic Models and Diffusion-based Adversarial Auto-Encoders [137.1060633388405]
  Diffusion-based generative models learn how to generate the data by inferring a reverse diffusion chain. We propose a faster and cheaper approach that adds noise not until the data become pure random noise. We show that the proposed model can be cast as an adversarial auto-encoder empowered by both the diffusion process and a learnable implicit prior.
  arXiv  Detail & Related papers  (2022-02-19T20:18:49Z)

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.