# Response Theory via Generative Score Modeling

arXiv: https://arxiv.org/abs/2402.01029 · HTML: https://mlsanity.com/paper/2402.01029/

## Key facts

- Cited by 3 papers in the map (data through 14 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.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Causal Machine Learning: A Survey and Open Problems](https://mlsanity.com/paper/2206.15475/) (2022)
- [Your diffusion model secretly knows the dimension of the data manifold](https://mlsanity.com/paper/2212.12611/) (2022)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Neural tuning and representational geometry](https://mlsanity.com/paper/2104.09743/) (2021)
- [Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data](https://mlsanity.com/paper/2012.06081/) (2020)
- [Unpaired Downscaling of Fluid Flows with Diffusion Bridges](https://mlsanity.com/paper/2305.01822/) (2023)
- [Deep Learning of Causal Structures in High Dimensions](https://mlsanity.com/paper/2212.04866/) (2022)
- [Large-scale nonlinear Granger causality: A data-driven, multivariate approach to recovering directed networks from short time-series data](https://mlsanity.com/paper/2009.04681/) (2020)
- [Multiplex PageRank](https://mlsanity.com/paper/1306.3576/) (2013)
- [High-dimensional inference: a statistical mechanics perspective](https://mlsanity.com/paper/2010.14863/) (2020)
- [Efficient state and parameter estimation for high-dimensional nonlinear system identification with application to MEG brain network modeling](https://mlsanity.com/paper/2104.02827/) (2021)

## Built on by (most cited first, 3 of 3)

- [Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling](https://mlsanity.com/paper/2504.13333/) (2025)
- [Reduced-Order Modeling of Cyclo-Stationary Time Series Using Score-Based Generative Methods](https://mlsanity.com/paper/2508.19448/) (2025)
- [Conditional Score-Based Modeling of Effective Langevin Dynamics](https://mlsanity.com/paper/2604.23952/) (2026)

## 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.