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Updated: Sep 19, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Generative diffusion models in infinite dimensions: a survey.

Giulio Franzese1, Pietro Michiardi1

  • 1Data Science, EURECOM, Biot, France.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 19, 2025
PubMed
Summary
This summary is machine-generated.

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This survey explores infinite-dimensional diffusion models for generating complex data. These models extend generative capabilities to function spaces, offering new solutions for inverse problems and data synthesis.

Area of Science:

  • Machine Learning
  • Probability Theory
  • Functional Analysis

Background:

  • Diffusion models excel in generating finite-dimensional data like images and audio.
  • Extending diffusion models to infinite-dimensional function spaces is an emerging research area.
  • Stochastic differential equations in Hilbert spaces provide the theoretical basis.

Purpose of the Study:

  • To provide a comprehensive overview of infinite-dimensional diffusion models.
  • To discuss theoretical foundations and practical applications.
  • To highlight connections and future research directions.

Main Methods:

  • Reviewing stochastic differential equations in Hilbert spaces.
  • Discussing generative models based on infinite-dimensional formalism.
Keywords:
Hilbert spacesgenerative diffusion modelsstochastic differential equations

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  • Surveying applications in function space modeling and inverse problems.

    • Main Results:

    • Infinite-dimensional diffusion models offer powerful generative capabilities for functional data.
    • These models are applicable to conditional generation and solving inverse problems.
    • Connections between different approaches and open problems are identified.

    Conclusions:

    • Infinite-dimensional diffusion models represent a significant advancement in generative modeling.
    • They provide a flexible framework for complex data generation and analysis.
    • Further research is needed to fully explore their potential in various scientific domains.