Operator-Informed Score Matching for Markov Diffusion Models
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
Diffusion models are typically trained using score matching, a learning objective agnostic to the underlying noising process that guides the model. This paper argues that Markov noising processes enjoy an advantage over alternatives, as the Markov operators that govern the noising process are well-understood. Specifically, by leveraging the spectral decomposition of the infinitesimal generator of the Markov noising process, we obtain parametric estimates of the score functions simultaneously for all marginal distributions, using only sample averages with respect to the data distribution. The resulting operator-informed score matching provides both a standalone approach to sample generation for low-dimensional distributions, as well as a recipe for better informed neural score estimators in high-dimensional settings.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 23 of its 60 references that are in the map. First posted on arXiv 13 Jun 2024.
Builds on
23 of 60 references.
Closest ancestors · 11
Same direction, newest first
- 2023Closed-Form Diffusion Models19 Oct
- 2022From Denoising Diffusions to Denoising Markov Models7 Nov
- 2022FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation9 Oct
- 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise19 Aug
- 2022Score-Based Generative Models Detect Manifolds2 Jun
- 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
- 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
- 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
- 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
- 2020Denoising Diffusion Probabilistic Models19 Jun
- 2020Improved Techniques for Training Score-Based Generative Models16 Jun
Other references · 12
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
- 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
- 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
- 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
- 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
- 2020Telescoping Density-Ratio Estimationcited by 108
- 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
- 2021Density Ratio Estimation via Infinitesimal Classificationcited by 59
- 2013Kernel Mean Estimation and Stein's Effectcited by 11
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- 2025Dimension-free Score Matching and Time Bootstrapping for Diffusion Models
- 2026First Learn, Then Memorize: The Spectral Bias of Diffusion Models
- 2026Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors
- 2025Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves
- 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
- 2024The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and its Applications