Stochastic Differential Equations

Also known as SDE

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21 papers in the last four weeks, up 320% on the four weeks before. 0.1% of all new papers.

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The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis
Jun 13, 2025Bernardo P. Schaeffer, Ricardo M. S. Rosa, Glauco ValleStochastic Differential Equations Diffusion Sampling
Instituto de Matem´atica, Universidade Federal do Rio de Janeiro
A Jump-Diffusion Framework for Irregular Time Series Generation
May 29, 2025O. Pfohl, J. Chemseddine, P. Hagemann +3Irregular Time-Series Modeling Stochastic Differential Equations
Department of Mathematics, Humboldt-Universität zu Berlin, 12489, Berlin, Germany · Department of Mathematics, Technische Universität Berlin, 10623, Berlin, Germany · Bundesanstalt für Materialforschung und -prüfung, 12205, Berlin, Germany +1
Rough Stochastic Pontryagin Maximum Principle and an Indirect Shooting Method
Feb 10, 2025Thomas LewStochastic Differential Equations Stochastic Optimal Control
Toyota Research Institute
Deep Operator BSDE: a Numerical Scheme to Approximate Solution Operators
Dec 4, 2024Pere Diaz-Lozano, Giulia Di NunnoStochastic Differential Equations
Department of Mathematics, University of Oslo, Oslo, Norway
Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs
Oct 18, 2024Takashi Furuya, Anastasis KratsiosStochastic Differential Equations PDE Solving
Doshisha University, Japan · Department of Mathematics McMaster University and Vector Institute, Canada
DeepSPoC: A Deep Learning Based Sequential Propagation of Chaos
Aug 29, 2024Kai Du, Yongle Xie, Tao Zhou +1Stochastic Differential Equations Neural PDE Solvers
Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200438, China. · Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China. · LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing, China.
Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data
Feb 22, 2024YongKyung Oh, Dong-Young Lim, Sungil KimIrregular Time-Series Modeling Time Series Imputation
Ulsan National Institute of Science and Technology, Republic of Korea
Deep learning based numerical approximation algorithms for stochastic partial differential equations
Dec 2, 2020Christian Beck, Sebastian Becker, Patrick Cheridito +2Stochastic Differential Equations Neural PDE Solvers
Department of Mathematics, ETH Zurich · School of Data Science and School of Artificial Intelligence,2025 The Chinese University of Hong Kong, Shenzhen (CUHK-Shenhen) · Applied Mathematics: Institute for Analysis and Numerics, University of Münster +1

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The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis

Bernardo P. Schaeffer, Ricardo M. S. Rosa, Glauco Valle

Instituto de Matem´atica, Universidade Federal do Rio de Janeiro

Stochastic Differential Equations Diffusion Sampling Score-Based Generative Modeling Diffusion Models

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Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary stochasticity function or a probability flow ODE, corresponding to setting this stochasticity function to zero. In this work, we investigate the effect of this stochasticity on the generation process through the evolution of Kullback-Leibler (KL) divergences, obtaining general KL divergence bounds and a novel analysis of the impact of the time-profile of the score error on model performance. For exact score functions, stochasticity has a contractive effect, decreasing KL divergence along the sampling trajectory. For approximate scores, however, a trade-off arises between correcting accumulated errors and amplifying current score errors, meaning stochasticity can either improve or degrade generation performance. Theoretical considerations indicate that the gain from stochasticity depends on the time-localization of the trained model error. We test this in experiments on both toy and benchmark data sets, also comparing the KL divergence evolution with the obtained bounds. We also present a fully analytical example, where all the relevant quantities can be computed, and the optimal stochasticity function can be characterized via an optimal control analysis.