FAST-Brain: A Flow-Aligned Spatio-Temporal Surrogate Brain Model

Shucheng Liu; Changchun Shi; Kai Zhang; Hongtu Zhu

cs.LGSep 28, 2026

FAST-Brain: A Flow-Aligned Spatio-Temporal Surrogate Brain Model

Authors: Shucheng Liu, Changchun Shi, Kai Zhang, Hongtu Zhu

Organizations: University of North Carolina at Chapel Hill · London School of Economics and Political Science

Abstract

Modeling resting-state functional magnetic resonance imaging (rs-fMRI) data is crucial for understanding brain-wide neural activity. However, traditional methods struggle to capture complex temporal dynamics over long horizons, to account for the brain's anatomical spatial structure, and to model high-dimensional ambient signals that lie on a low-dimensional intrinsic subspace. We propose FAST-Brain, a unified flow-aligned spatio-temporal surrogate brain model that addresses all three challenges. At its core is a flow-aligned generative framework that directly predicts the clean blood-oxygen-level-dependent (BOLD) signal, paired with a graph convolutional network that captures spatial structural constraints and a Transformer that models long-range temporal dependencies. Theoretically, we show that under a low-dimensional subspace assumption, the approximation error of our model scales with the intrinsic dimension rather than the ambient dimension, which justifies our direct modeling of the BOLD signal. Extensive experiments on synthetic and Human Connectome Project datasets demonstrate that FAST-Brain achieves state-of-the-art performance in recovering functional connectivity, effective connectivity, and the implicit low-dimensional signal subspace.

Figures & tables

Figure 1: Model architecture of FAST-Brain. The framework integrates flow-aligned clean-signal prediction with a temporal Transformer and a spatial multi-graph GCN to generate surrogate BOLD dynamics for downstream connectivity and subspace analysis.

Dataset	Metric	NPI	TimeDiff	SSSD	DiffusionTS	FlowTS	DSFM	FAST-Brain
RNN	Correlation $\uparrow$	0.547 ±0.073	0.431 ±0.003	0.822 ±0.010	0.824 ±0.006	0.846 ±0.005	0.695 ±0.008	0.938 ±0.006
RNN	MAE $\downarrow$	0.322 ±0.075	0.364 ±0.003	0.050 ±0.002	0.062 ±0.001	0.059 ±0.001	0.087 ±0.004	0.028 ±0.002
SDDEs	Correlation $\uparrow$	0.789 ±0.009	0.821 ±0.000	0.890 ±0.001	0.886 ±0.018	0.830 ±0.008	0.642 ±0.008	0.975 ±0.009
SDDEs	MAE $\downarrow$	0.332 ±0.006	0.311 ±0.000	0.170 ±0.001	0.169 ±0.012	0.275 ±0.003	0.304 ±0.004	0.115 ±0.023
HCP	Correlation $\uparrow$	0.634 ±0.074	0.344 ±0.002	0.186 ±0.002	0.474 ±0.004	0.726 ±0.008	0.692 ±0.035	0.938 ±0.005
HCP	MAE $\downarrow$	0.212 ±0.030	0.386 ±0.001	0.402 ±0.000	0.201 ±0.027	0.280 ±0.005	0.199 ±0.032	0.073 ±0.008

Table 1: Functional connectivity recovery across three datasets.

Method	Correlation $\uparrow$	AUROC $\uparrow$	AUPRC $\uparrow$
NPI	0.065 ±0.063	0.466 ±0.061	0.093 ±0.020
TimeDiff	0.013 ±0.046	0.487 ±0.053	0.102 ±0.023
SSSD	0.828 ±0.005	0.851 ±0.005	0.736 ±0.005
DiffusionTS	0.716 ±0.021	0.848 ±0.030	0.600 ±0.049
FlowTS	0.851 ±0.004	0.916 ±0.006	0.810 ±0.007
DSFM	-0.006 ±0.022	0.462 ±0.028	0.093 ±0.010

Table 2: Effective connectivity analysis on RNN dataset.

Metric	NPI	TimeDiff	SSSD	DiffusionTS	FlowTS	DSFM	FAST-Brain
CRPS $\downarrow$	0.248 ±0.002	0.213 ±0.000	0.217 ±0.000	0.158 ±0.000	0.168 ±0.000	0.176 ±0.000	0.154 ±0.000
QICE $\downarrow$	0.160 ±0.000	0.140 ±0.001	0.144 ±0.000	0.011 ±0.000	0.069 ±0.000	0.007 ±0.000	0.005 ±0.000
ProbCorr $\downarrow$	0.317 ±0.004	0.314 ±0.000	0.264 ±0.000	0.266 ±0.000	0.280 ±0.000	0.305 ±0.001	0.261 ±0.000
Conditional FID $\downarrow$	3.516 ±0.040	8.384 ±1.238	2.522 ±0.012	1.916 ±0.002	2.020 ±0.002	2.812 ±0.387	1.856 ±0.003

Table 3: Conditional generation quality on the RNN dataset.

Dataset	Metric	FAST-Brain	w/o GCN	$\epsilon$ -pred.	$v$ -pred.
RNN	Corr $\uparrow$	0.938 ±0.006	0.932 ±0.006	0.928 ±0.011	0.919 ±0.014
RNN	MAE $\downarrow$	0.028 ±0.002	0.029 ±0.002	0.028 ±0.002	0.032 ±0.003
SDDEs	Corr $\uparrow$	0.975 ±0.009	0.827 ±0.002	0.862 ±0.004	0.822 ±0.004
SDDEs	MAE $\downarrow$	0.115 ±0.023	0.305 ±0.001	0.130 ±0.004	0.292 ±0.003
HCP	Corr $\uparrow$	0.938 ±0.005	0.867 ±0.015	0.799 ±0.009	0.856 ±0.014
HCP	MAE $\downarrow$	0.073 ±0.008	0.133 ±0.017	0.313 ±0.004	0.209 ±0.017

Table 4: Ablation study on functional connectivity recovery.

Figure 2: Latent-space and value-distribution analyses on the SDDEs dataset.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 3: Qualitative visualization of functional connectivity recovery on the RNN, SDDEs, and HCP datasets. From left to right, the columns correspond to RNN, SDDEs, and HCP. The top row shows empirical FC matrices, and the bottom row shows FC matrices generated by FAST-Brain.

Metric	NPI	TimeDiff	SSSD	DiffusionTS	FlowTS	DSFM	FAST-Brain
CRPS $\downarrow$	0.213 ±0.002	0.253 ±0.000	0.340 ±0.000	0.263 ±0.001	0.411 ±0.001	0.240 ±0.000	0.198 ±0.003
QICE $\downarrow$	0.160 ±0.000	0.125 ±0.000	0.035 ±0.000	0.023 ±0.000	0.105 ±0.000	0.152 ±0.000	0.019 ±0.002
ProbCorr $\downarrow$	0.310 ±0.006	0.215 ±0.000	0.422 ±0.000	0.238 ±0.001	0.539 ±0.001	0.247 ±0.000	0.248 ±0.003
Conditional FID $\downarrow$	6.788 ±0.348	4.302 ±0.043	19.256 ±0.066	3.741 ±0.010	3.520 ±0.005	9.174 ±1.367	5.841 ±0.049

Appendix

Table 5: Conditional generation metrics in SDDEs.

Metric	NPI	TimeDiff	SSSD	DiffusionTS	FlowTS	DSFM	FAST-Brain
CRPS $\downarrow$	0.710 ±0.017	0.829 ±0.000	0.580 ±0.000	0.640 ±0.000	0.634 ±0.002	0.566 ±0.002	0.559 ±0.002
QICE $\downarrow$	0.160 ±0.000	0.155 ±0.000	0.008 ±0.001	0.123 ±0.000	0.095 ±0.001	0.028 ±0.000	0.027 ±0.000
ProbCorr $\downarrow$	0.464 ±0.006	0.485 ±0.000	0.566 ±0.000	0.494 ±0.000	0.551 ±0.001	0.553 ±0.001	0.450 ±0.001
Conditional FID $\downarrow$	81.185 ±1.924	72.006 ±1.618	21.527 ±0.193	15.274 ±0.013	15.909 ±0.102	31.333 ±1.290	13.882 ±0.071

Appendix

Table 6: Conditional generation metrics in HCP.

Metric	NPI	TimeDiff	SSSD	DiffusionTS	FlowTS	DSFM	FAST-Brain
Discriminative Score $\downarrow$	0.330 ±0.138	0.360 ±0.145	0.165 ±0.092	0.200 ±0.097	0.115 ±0.063	0.100 ±0.081	0.085 ±0.059
Predictive Score $\downarrow$	0.230 ±0.006	0.211 ±0.002	0.211 ±0.002	0.213 ±0.002	0.208 ±0.001	0.211 ±0.002	0.209 ±0.003
Context-FID $\downarrow$	1.722 ±0.666	1.508 ±0.493	0.234 ±0.052	0.253 ±0.072	0.154 ±0.021	0.619 ±0.060	0.121 ±0.029
Correlational Score $\downarrow$	0.380 ±0.102	0.217 ±0.003	0.054 ±0.001	0.058 ±0.003	0.055 ±0.001	0.067 ±0.002	0.038 ±0.001

Appendix

Table 7: Unconditional generation metrics in RNN.

Metric	NPI	TimeDiff	SSSD	DiffusionTS	FlowTS	DSFM	FAST-Brain
Discriminative Score $\downarrow$	0.270 ±0.149	0.250 ±0.175	0.350 ±0.143	0.310 ±0.158	0.340 ±0.174	0.370 ±0.078	0.120 ±0.108
Predictive Score $\downarrow$	0.248 ±0.011	0.283 ±0.006	0.510 ±0.023	0.399 ±0.030	0.550 ±0.011	0.442 ±0.020	0.334 ±0.020
Context-FID $\downarrow$	10.344 ±0.303	13.530 ±0.786	23.649 ±3.418	10.998 ±2.183	15.747 ±0.696	42.045 ±3.913	6.532 ±0.806
Correlational Score $\downarrow$	0.531 ±0.006	0.418 ±0.001	0.379 ±0.002	0.360 ±0.038	0.480 ±0.002	0.398 ±0.009	0.329 ±0.015

Appendix

Table 8: Unconditional generation metrics in SDDEs.

Metric	NPI	TimeDiff	SSSD	DiffusionTS	FlowTS	DSFM	FAST-Brain
Discriminative Score $\downarrow$	0.287 ±0.115	0.338 ±0.113	0.262 ±0.098	0.275 ±0.109	0.300 ±0.083	0.263 ±0.118	0.200 ±0.115
Predictive Score $\downarrow$	0.746 ±0.019	0.776 ±0.008	0.795 ±0.010	0.796 ±0.010	0.692 ±0.006	0.702 ±0.012	0.740 ±0.034
Context-FID $\downarrow$	66.432 ±9.314	93.019 ±6.584	70.196 ±2.164	85.045 ±5.285	58.411 ±4.880	82.183 ±9.055	59.574 ±3.787
Correlational Score $\downarrow$	0.258 ±0.053	0.361 ±0.001	0.339 ±0.001	0.242 ±0.020	0.282 ±0.002	0.210 ±0.015	0.162 ±0.004

Appendix

Table 9: Unconditional generation metrics in HCP.

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Functional Magnetic Resonance Imaging (fMRI) provides non-invasive access to dynamic brain activity by measuring blood oxygen level-dependent (BOLD) signals over time. However, the resource-intensive nature of fMRI acquisition limits the availability of high-fidelity samples required for data-driven brain analysis models. While modern generative models can synthesize fMRI data, they often remain challenging in replicating their inherent non-stationarity, intricate spatiotemporal dynamics, and physiological variations of raw BOLD signals. To address these challenges, we propose Dual-Spectral Flow Matching (DSFM), a novel fMRI generative framework that cascades dual frequency representation of BOLD signals with spectral flow matching. Specifically, our framework first converts BOLD signals into a wavelet decomposition map via a discrete wavelet transform (DWT) to capture globalized transient and multi-scale variations, and projects into the discrete cosine transform (DCT) space across brain regions and time to exploit localized energy compaction of low-frequency dominant BOLD coefficients. Subsequently, a spectral flow matching model is trained to generate class-conditioned cosine-frequency representation. The generated samples are reconstructed through inverse DCT and inverse DWT operations to recover physiologically plausible time-domain BOLD signals. This dual-transform approach imposes structured frequency priors and preserves key physiological brain dynamics. Ultimately, we demonstrate the efficacy of our approach through improved downstream fMRI-based brain network classification. The code is available at https://github.com/htew0001/DSFM.git .

Abstract

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