Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians

• URL: http://arxiv.org/abs/2312.14977v1
• Date: Thu, 21 Dec 2023 20:20:52 GMT
• Title: Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians
• Authors: Catherine F. Higham and Desmond J. Higham and Peter Grindrod
• Abstract summary: Diffusion models offer state of the art performance in generative AI for images. We provide a brief introduction to diffusion models for applied mathematicians and statisticians.
• Score: 3.069335774032178
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Generative artificial intelligence (AI) refers to algorithms that create synthetic but realistic output. Diffusion models currently offer state of the art performance in generative AI for images. They also form a key component in more general tools, including text-to-image generators and large language models. Diffusion models work by adding noise to the available training data and then learning how to reverse the process. The reverse operation may then be applied to new random data in order to produce new outputs. We provide a brief introduction to diffusion models for applied mathematicians and statisticians. Our key aims are (a) to present illustrative computational examples, (b) to give a careful derivation of the underlying mathematical formulas involved, and (c) to draw a connection with partial differential equation (PDE) diffusion models. We provide code for the computational experiments. We hope that this topic will be of interest to advanced undergraduate students and postgraduate students. Portions of the material may also provide useful motivational examples for those who teach courses in stochastic processes, inference, machine learning, PDEs or scientific computing.

Related papers

• MING: A Functional Approach to Learning Molecular Generative Models [46.189683355768736]
  This paper introduces a novel paradigm for learning molecule generative models based on functional representations. We propose Molecular Implicit Neural Generation (MING), a diffusion-based model that learns molecular distributions in function space.
  arXiv  Detail & Related papers  (2024-10-16T13:02:02Z)
• 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)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Self-Supervised Learning with Lie Symmetries for Partial Differential Equations [25.584036829191902]
  We learn general-purpose representations of PDEs by implementing joint embedding methods for self-supervised learning (SSL) Our representation outperforms baseline approaches to invariant tasks, such as regressing the coefficients of a PDE, while also improving the time-stepping performance of neural solvers. We hope that our proposed methodology will prove useful in the eventual development of general-purpose foundation models for PDEs.
  arXiv  Detail & Related papers  (2023-07-11T16:52:22Z)
• Score-based Diffusion Models in Function Space [140.792362459734]
  Diffusion models have recently emerged as a powerful framework for generative modeling. We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
  arXiv  Detail & Related papers  (2023-02-14T23:50:53Z)
• Generative Diffusion Models on Graphs: Methods and Applications [50.44334458963234]
  Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks. Graph generation is a crucial computational task on graphs with numerous real-world applications.
  arXiv  Detail & Related papers  (2023-02-06T06:58:17Z)
• Advancing Reacting Flow Simulations with Data-Driven Models [50.9598607067535]
  Key to effective use of machine learning tools in multi-physics problems is to couple them to physical and computer models. The present chapter reviews some of the open opportunities for the application of data-driven reduced-order modeling of combustion systems.
  arXiv  Detail & Related papers  (2022-09-05T16:48:34Z)
• Process Discovery Using Graph Neural Networks [2.6381163133447836]
  We introduce a technique for training an ML-based model D using graphal neural networks. D translates a given input event log into a sound Petri net. We show that training D on synthetically generated pairs of input logs and output models allows D to translate previously unseen synthetic and several real-life event logs into sound.
  arXiv  Detail & Related papers  (2021-09-13T10:04:34Z)
• The data-driven physical-based equations discovery using evolutionary approach [77.34726150561087]
  We describe the algorithm for the mathematical equations discovery from the given observations data. The algorithm combines genetic programming with the sparse regression. It could be used for governing analytical equation discovery as well as for partial differential equations (PDE) discovery.
  arXiv  Detail & Related papers  (2020-04-03T17:21:57Z)

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.