mlsanityData to 7 Oct 2026

Generative Diffusion From An Action Principle

arXiv 2310.04490 ↗First posted 6 Oct 2023cs.LG physics.class-phcited by 5

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability distribution of a given data set, also called the score. By casting reverse diffusion as an optimal control problem, we show that score matching can be derived from an action principle, like the ones commonly used in physics. We use this insight to demonstrate the connection between different classes of diffusion models.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 14 of its 40 references that are in the map. First posted on arXiv 6 Oct 2023.

Builds on

14 of 40 references.

Closest ancestors · 8

Same direction, newest first

  1. 2022An optimal control perspective on diffusion-based generative modeling2 Nov
  2. 2022Riemannian Score-Based Generative Modelling6 Feb
  3. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  4. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  5. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  6. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  7. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  8. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 6

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  4. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  5. 2017Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Netcited by 30
  6. 2022On local entropy, stochastic control and deep neural networkscited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 0; 2026: 2.

5 papers.

  1. 2024Understanding Diffusion Models by Feynman's Path Integralcited by 13
  2. 2024Neural Entropycited by 7
  3. 2024Diffusion Density Estimatorscited by 2
  4. 2026A Unified Kullback--Leibler Divergence Analysis of Generative Diffusion Models via Entropy Production Ratecited by 0
  5. 2026The Loss Floor of Denoising Score Matching: Fisher Geometry from Schr"odinger Bridgescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
  2. 2023Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians
  3. 2025Generative diffusion models from a PDE perspective
  4. 2025The Principles of Diffusion Models
  5. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  6. 2025Are We Really Learning the Score Function? Reinterpreting Diffusion Models Through Wasserstein Gradient Flow Matching
  7. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models
  8. 2024GUD: Generation with Unified Diffusion