# GRFBrain: Graph-Structured Rectified Flows for EEG Dynamic Modeling

arXiv: https://arxiv.org/abs/2609.37934 · HTML: https://mlsanity.com/paper/2609.37934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 31 of its 35 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Unsupervised Time-Series Representation Learning with Iterative Bilinear Temporal-Spectral Fusion](https://mlsanity.com/paper/2202.04770/) (2022)
- [The Temple University Hospital Seizure Detection Corpus](https://mlsanity.com/paper/1801.08085/) (2018)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [Self-Supervised Graph Neural Networks for Improved Electroencephalographic Seizure Analysis](https://mlsanity.com/paper/2104.08336/) (2021)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [Modeling Multivariate Biosignals With Graph Neural Networks and Structured State Space Models](https://mlsanity.com/paper/2211.11176/) (2022)
- [Temporal Graph Convolutional Networks for Automatic Seizure Detection](https://mlsanity.com/paper/1905.01375/) (2019)
- [Neural Memory Networks for Seizure Type Classification](https://mlsanity.com/paper/1912.04968/) (2019)
- [Tokenizing Single-Channel EEG with Time-Frequency Motif Learning](https://mlsanity.com/paper/2502.16060/) (2025)
- [Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry](https://mlsanity.com/paper/2505.18193/) (2025)
- [BrainODE: Dynamic Brain Signal Analysis via Graph-Aided Neural Ordinary Differential Equations](https://mlsanity.com/paper/2405.00077/) (2024)
- [REST: Efficient and Accelerated EEG Seizure Analysis through Residual State Updates](https://mlsanity.com/paper/2406.16906/) (2024)
- [Designing a Conditional Prior Distribution for Flow-Based Generative Models](https://mlsanity.com/paper/2502.09611/) (2025)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [Better Source, Better Flow: Learning Condition-Dependent Source Distribution for Flow Matching](https://mlsanity.com/paper/2602.05951/) (2026)
- [EvoBrain: Dynamic Multi-Channel EEG Graph Modeling for Time-Evolving Brain Networks](https://mlsanity.com/paper/2509.15857/) (2025)
- [CAR-Flow: Condition-Aware Reparameterization Aligns Source and Target for Better Flow Matching](https://mlsanity.com/paper/2509.19300/) (2025)
- [Topological Flow Matching](https://mlsanity.com/paper/2606.15897/) (2026)
- [Dynamic Structural Similarity on Graphs](https://mlsanity.com/paper/1805.01419/) (2018)
- [ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networks](https://mlsanity.com/paper/2602.23285/) (2026)

## Abstract (arXiv)

Forecasting time-varying functional connectivity from electroencephalography (EEG) requires modeling both history-dependent trends and structured variability across channels. Conditional flow matching provides a framework for distributional forecasting, yet it remains unclear whether graph-informed source distributions offer practical advantages over isotropic noise and strong deterministic predictors. We introduce a graph-structured residual flow framework that separates conditional mean prediction from stochastic residual transport. A history-only predictor estimates the future connectivity graph, while a graph Gaussian source encodes dependencies derived from past connectivity through a Laplacian-based covariance. A conditional velocity field transports source samples to future graph residuals, with transport time explicitly distinguished from physical EEG time. Our study identifies the conditions and controls needed to distinguish useful residual transport from improvements attributable to deterministic prediction, learned representations, and sampling effects.