Information-Theoretic Diffusion
- URL: http://arxiv.org/abs/2302.03792v1
- Date: Tue, 7 Feb 2023 23:03:07 GMT
- Title: Information-Theoretic Diffusion
- Authors: Xianghao Kong, Rob Brekelmans, Greg Ver Steeg
- Abstract summary: Denoising diffusion models have spurred significant gains in density modeling and image generation.
We introduce a new mathematical foundation for diffusion models inspired by classic results in information theory.
- Score: 18.356162596599436
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Denoising diffusion models have spurred significant gains in density modeling
and image generation, precipitating an industrial revolution in text-guided AI
art generation. We introduce a new mathematical foundation for diffusion models
inspired by classic results in information theory that connect Information with
Minimum Mean Square Error regression, the so-called I-MMSE relations. We
generalize the I-MMSE relations to exactly relate the data distribution to an
optimal denoising regression problem, leading to an elegant refinement of
existing diffusion bounds. This new insight leads to several improvements for
probability distribution estimation, including theoretical justification for
diffusion model ensembling. Remarkably, our framework shows how continuous and
discrete probabilities can be learned with the same regression objective,
avoiding domain-specific generative models used in variational methods. Code to
reproduce experiments is provided at http://github.com/kxh001/ITdiffusion and
simplified demonstration code is at
http://github.com/gregversteeg/InfoDiffusionSimple.
Related papers
- Constrained Diffusion Models via Dual Training [80.03953599062365]
We develop constrained diffusion models based on desired distributions informed by requirements.
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) - Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling [2.1779479916071067]
We introduce a novel framework that enhances diffusion models by supporting a broader range of forward processes.
We also propose a novel parameterization technique for learning the forward process.
Results underscore NFDM's versatility and its potential for a wide range of applications.
arXiv Detail & Related papers (2024-04-19T15:10:54Z) - Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory [87.00653989457834]
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning.
Despite the empirical success, theory of conditional diffusion models is largely missing.
This paper bridges the gap by presenting a sharp statistical theory of distribution estimation using conditional diffusion models.
arXiv Detail & Related papers (2024-03-18T17:08:24Z) - 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) - 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) - 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) - 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) - An optimal control perspective on diffusion-based generative modeling [9.806130366152194]
We establish a connection between optimal control and generative models based on differential equations (SDEs)
In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals.
We develop a novel diffusion-based method for sampling from unnormalized densities.
arXiv Detail & Related papers (2022-11-02T17:59:09Z) - 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)
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.