A Malliavin-Gamma calculus approach to Score Based Diffusion Generative models for random fields
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
We adopt a Gamma and Malliavin Calculi point of view in order to generalize Score-based diffusion Generative Models (SGMs) to an infinite-dimensional abstract Hilbertian setting. Particularly, we define the forward noising process using Dirichlet forms associated to the Cameron-Martin space of Gaussian measures and Wiener chaoses; whereas by relying on an abstract time-reversal formula, we show that the score function is a Malliavin derivative and it corresponds to a conditional expectation. This allows us to generalize SGMs to the infinite-dimensional setting. Moreover, we extend existing finite-dimensional entropic convergence bounds to this Hilbertian setting by highlighting the role played by the Cameron-Martin norm in the Fisher information of the data distribution. Lastly, we specify our discussion for spherical random fields, considering as source of noise a Whittle-Mat'ern random spherical field.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 21 of its 44 references that are in the map. First posted on arXiv 19 May 2025.
Builds on
21 of 44 references.
Closest ancestors · 14
Same direction, newest first
- 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients6 May
- 2025Malliavin Calculus for Score-based Diffusion Models21 Mar
- 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance4 Jan
- 2024An analysis of the noise schedule for score-based generative models7 Feb
- 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptions23 Aug
- 2023Manifold Diffusion Fields24 May
- 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation8 Mar
- 2023Infinite-Dimensional Diffusion Models20 Feb
- 2023Score-based Diffusion Models in Function Space14 Feb
- 2022Convergence of score-based generative modeling for general data distributions26 Sep
- 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
- 2021Diffusion Models Beat GANs on Image Synthesis11 May
2 more
Other references · 7
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
- 2024Continuous Ensemble Weather Forecasting with Diffusion modelscited by 30
- 2022Posterior samples of source galaxies in strong gravitational lenses with score-based priorscited by 20
- 2025Conditioning Diffusions Using Malliavin Calculuscited by 15
- 2025A Unified Approach to Analysis and Design of Denoising Markov Modelscited by 12
- 2023Stochastic Super-resolution of Cosmological Simulations with Denoising Diffusion Modelscited by 4
- 2023Removing Dust from CMB Observations with Diffusion Modelscited by 2
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.
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Close in wording, no citation either way
- 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
- 2026Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs
- 2026A Stochastic Analysis Perspective on Diffusion Models
- 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
- 2023Improved Convergence of Score-Based Diffusion Models via Prediction-Correction
- 2022Diffusion Generative Models in Infinite Dimensions
- 2024Discrete vs. Continuous Trade-offs for Generative Models
- 2025A PDE Perspective on Generative Diffusion Models