A Complete Decomposition of Stochastic Differential Equations
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Abstract (arXiv)
We show that any stochastic differential equation with prescribed time-dependent marginal distributions admits a decomposition into three components: a unique scalar field governing marginal evolution, a symmetric positive-semidefinite diffusion matrix field and a skew-symmetric matrix field.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 10 of its 26 references that are in the map. First posted on arXiv 12 Jan 2026.
Builds on
10 of 26 references.
References · 10
- 2020Denoising Diffusion Probabilistic Modelscited by 21,076
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
- 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
- 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 292
- 2017A Conceptual Introduction to Hamiltonian Monte Carlocited by 209
- 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 183
- 2015A Complete Recipe for Stochastic Gradient MCMCcited by 146
- 2019On the geometry of Stein variational gradient descentcited by 82
- 2016Ensemble preconditioning for Markov chain Monte Carlo simulationcited by 16
- 2024Scalable Bayesian Learning with posteriorscited by 13
Built on by
Citing papers per year: 2026: 1.
1 paper.