Response Theory via Generative Score Modeling
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT). The methodology enables accurate estimation of system responses, including those with non-Gaussian statistics. We numerically validate our approach using time-series data from three different stochastic partial differential equations of increasing complexity: an Ornstein-Uhlenbeck process with spatially correlated noise, a modified stochastic Allen-Cahn equation, and the 2D Navier-Stokes equations. We demonstrate the improved accuracy of the methodology over conventional methods and discuss its potential as a versatile tool for predicting the statistical behavior of complex dynamical systems.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 19 of its 71 references that are in the map. First posted on arXiv 1 Feb 2024.
Builds on
19 of 71 references.
Closest ancestors · 4
Same direction, newest first
- 2022Your diffusion model secretly knows the dimension of the data manifold23 Dec
- 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 · 15
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- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
- 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
- 2019Machine Learning for Fluid Mechanicscited by 380
- 2022Causal Machine Learning: A Survey and Open Problemscited by 107
- 2023Discovering Causal Relations and Equations from Datacited by 33
- 2021Neural tuning and representational geometrycited by 31
- 2020Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Datacited by 22
- 2023Unpaired Downscaling of Fluid Flows with Diffusion Bridgescited by 21
- 2022Deep Learning of Causal Structures in High Dimensionscited by 20
- 2020Large-scale nonlinear Granger causality: A data-driven, multivariate approach to recovering directed networks from short time-series datacited by 12
Built on by
Citing papers per year: 2025: 2; 2026: 1.
3 papers.
- 2025Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modelingcited by 3
- 2025Reduced-Order Modeling of Cyclo-Stationary Time Series Using Score-Based Generative Methodscited by 1
- 2026Conditional Score-Based Modeling of Effective Langevin Dynamicscited by 0
- 2026Conditional Score-Based Modeling of Effective Langevin Dynamics27 Apr 2026
- 2025Reduced-Order Modeling of Cyclo-Stationary Time Series Using Score-Based Generative Methods26 Aug 2025
- 2025Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling17 Apr 2025
Similar, not cited
Close in wording, no citation either way
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- 2026Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs
- 2024Generative Learning for Forecasting the Dynamics of Complex Systems
- 2025Stochastic generative methods for stable and accurate closure modeling of chaotic dynamical systems
- 2023Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems
- 2023Score-based Data Assimilation
- 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
- 2025Wasserstein Convergence of Critically Damped Langevin Diffusions