Synthesizing Realistic fMRI: A Physiological Dynamics-Driven Hierarchical Diffusion Model for Efficient fMRI Acquisition
Authors: Yufan Hu
Yujiang
Wuyang Li
Yixuan Yuan
Venue: ICLR 2025 Poster (2025)
Keywords: Time Series
Diffusion
Primary area: learning on time series and dynamical systems

Abstract: Functional magnetic resonance imaging (fMRI) is essential for mapping brain activity but faces challenges like lengthy acquisition time and sensitivity to patient movement, limiting its clinical and machine learning applications. While generative models such as diffusion models can synthesize fMRI signals to alleviate these issues, they often underperform due to neglecting the brain's complex structural and dynamic properties.
To address these limitations, we propose the Physiological Dynamics-Driven Hierarchical Diffusion Model, a novel framework integrating two key brain physiological properties into the diffusion process: brain hierarchical regional interactions and multifractal dynamics. 
To model complex interactions among brain regions, we construct hypergraphs based on the prior knowledge of brain functional parcellation reflected by resting-state functional connectivity (rsFC). This enables the aggregation of fMRI signals across multiple scales and generates hierarchical signals. 
Additionally, by incorporating the prediction of two key dynamics properties of fMRI—the multifractal spectrum and generalized Hurst exponent—our framework effectively guides the diffusion process, ensuring the preservation of the scale-invariant characteristics inherent in real fMRI data.
Our framework employs progressive diffusion generation, with signals representing broader brain region information conditioning those that capture localized details, and unifies multiple inputs during denoising for balanced integration.
Experiments demonstrate that our model generates physiologically realistic fMRI signals, potentially reducing acquisition time and enhancing data quality, benefiting clinical diagnostics and machine learning in neuroscience.

Published as a conference paper at ICLR 2025
SYNTHESIZING REALISTIC FMRI: A PHYSIOLOGI- CAL DYNAMICS-DRIVES HIERARCHICAL DIFFUSION MODEL FOR EFFICIENT FMRI ACQUISITION
Yufan Hu, Yu Jiang, Wuyang Li, Yixuan Yuan*
The Chinese University of Hong Kong
yufanhuelink ochk.edu. hk, yujiangBcuhk. edu. hk, wymanbest@outlook com, yxyuanêee. cuhk. edu. hk
ABSTRACT
Functional magnetic resonance imaging (IMRI) is essential for mapping brain ac- tivity but faces challenges like lengthy acquisition time and sensitivity to patient movement, limiting its clinical and machine learning applications. While gen- erative models such as diffusion models can synthesize fMRI signals to allevi- ate these issues, they often underperform due to neglecting the brain's 's complex structural and dynamic properties. To address these limitations, we propose the Physiological Dynamics-Driven Hierarchical Diffusion Model, novel framework integrating two key brain physiological properties into the diffusion process: brain hierarchical regional interactions and multifractal dynamics. To model complex interactions among brain regions, we construct hypergraphs based on the prior knowledge of brain functional parcellation reflected by resting-stane state functional connectivity (rsFC). This enables the aggregation of fMRI signals across multi- ple scales and generates hierarchical signals. Additionally, by incorporating the prediction of two key dynamics properties of fMRI-the the multifractal spectrum and generalized Hurst exponent- our framework effectively guides the diffusion process, emsuring the preservation of the
characteristics inherent in real fMRI data. Our framework employs progressive diffusion generation, with signals representing broader brain region information conditioning those that cap- ture localized details, and unifies multiple inputs during denoising for balanced integration. Experiments demonstrate that our model generates physiologically realistic fMRI signals, potentially reducing acquisition time and enhancing data quality, benefiting clinical diagnostics and machine learning in neuroscience. Our code is available at https://github.com wtaptlhuubboo/CCCCCCC SOOOK-AAM-Grooan Gro.M/DDou//D---iii
INTRODUCTION
Functional magnetic resonance imaging (fMRI) is non-invasive neuroimaging technique that cap- tures spatio-temporal patterns of blood oxygenation in the active brain (D Esposito et al. 2003). Brain fMRI signals encapsulate the full spectrum intrinsic functional networks and exhibit highly complex fluctuating patterns, providing very accurate information of neural activity (Strangman jet al. 2002). Compared to other medical modalities, fMRI offers superior precision in predicting and diagnosing various neurological and psychiatric conditions (Matthews et al. (0066..
Despite its utility, fMRI data also presents unique challenges, particularly during acquisition. A stan- dard fMRT scan is highly time-consuming. For example, in the data collection process of Human Connectome Project (HCP), a resting-state fMRI sean lasts 60 minutes, divided into four 15-minute sessions (ann Essen et al., 2012). While necessary for capturing comprehensive brain activity, these long sessions can be physically taxing for participants. Additionally, IMRI scans impose strict re- quirements on patient stillness, which is particularly difficult for infants or those unable stay still for long periods. as even minor movements can introduce noise and artifacts, reducing data qual- ity (Power et al. 2014 Bollmann Barth 2021). These challenges significantly limit its broader
"Correspondence

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application in clinical diagnosis and machine learning algorithm development. As result, there is growing need for methods to generate and impute fMRI time series signals, which can reduce acqui- sition times and optimize the quality of the acquired data. Notably, diffusion models have recently emerged as a prominent generative approach and show promise in their generative capacity within
the time series domain (Rasul et al., 2021 Shen et al.. 2024 Fan et al. 2024 Li et al. 2024b a)
highlighting their potential for further exploration in IMRI signal generation.
While showing potential for application, diffusion models often underperform when applied to brain IMRI signal generation, as most advanced methods are designed for task-agnostic generation and ne- glect two key intrinsic physical properties of brain fMRI signals. First, they tend to treat fMRI data from each gegion-of-interee (ROI) independently, overlooking the high-dimensional interactions be- tween signals from different ROIs (Logothetis] 2008) [Balley et al., 2017), which are indispensable for examining hypothesized disconnectivity effects in neurodegenerative and psychiatric brain dis- eases (Van Den Heuvel & Poll 2010). To address this limitation, we incorporate brain regional interactions using hypergraph (see Figure D. which is constructed based brain rsFC" Second, while these models excel at capturing temporal trends, they often fail to account for the unique physi- ological patterns and dynamics properties of brain signals, specifically fractal characteristics. These dynamics arise from repeated, scale-free information exchange between brain regions, generating fMRI signals that exhibit self-similarity (He 2014). Scale-free dynamics in fMRI have been shown to vary across brain networks and behavioral conditions (Ciuciu et al. 2012). as well as change with age (Suckling et al., 2008), arousal states (Tagliazucchi al.] 2013)). and disease processes (Maxim) iet 2005). Analyzing these dynamics provides critical insights into the brain mechanisms that underlie cognition and behavior (Ciuciu al. 2014 He et al., 2023: 2024). To overeome this short- coming, we integrate these dynamics properties into our model, emphasizing the multifractal nature of brain activity. By introducing these two fundamental aspects of brain, our method achieves more realistic and precise fMRI signal generation, better aligning with the brain's physiological reality.
The contribution of this paper can be summarized as follows: We propose a novel framework for generating brain fMRI time series signals, grounded in the above two key observations about fMRI signals, brain regional interactions, and multifractal dynamics. This framework, called the Physio- logical Dynnaiccs-riven Hierarchical Diffusion Model, is composed of three main components:
1.
The Hypergraph- bassed Hierarchical Signals Generator: To incorporate intricate interdependen- cies between brain regions, we model brain rsFC as a hypergraph structure that captures complex interactions among signals of ROIs. This component aggregates fMRI signals based the in- trinsic brain functional connectivity matrix across multiple brain regions, producing hicrarchical fMRI signals that encapsulate information at various scales.
2. The Dynamics Properties Guiding Module: This module is designed to incorporate the dynamics properties of brain activity, specifically utilizing the multifractal characteristics of fMRi signals into diffusion generation process. includes a predictor that estimates the multifractal spectrum and the generalized Hurst exponent of the IMRI series. The predicted multifractal characteris- ties are then projected as a conditioning input to guide the diffusion process, ensuring that the generated signals maintain the complex, scale- invariant properties observed in real fMRI data.
3. The Cross-brain Region Guiding Progressive Diffusion Model: To ensure complementary signals across different brain region ranges, progressive generation employed, where broader regional signal trends are used as conditioning inputs to guide the detailed signals of more localized brain areas. Finally, we dynamically unifies multiple conditioning inputs during the denoising phase of diffusion, ensuring balanced and coherent integration of multiple conditions.
2 PRELIMINARIES
2.1 FUNCTIONAL CONNECTIVITY OF FMRI SIGNALS.
The human brain is complex network of functionally and structurally interconnected regions. Even at rest, there is a high level of ongoing functional connectivity and continuous information process- ing between the hemispheric motor cortices and between other well-established functional networks,
brain resting-state functional connectivity (rsFC) reflects the synchronized activity and communication between brain regions during resting state.
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such the primary visual, auditory, and higher-order cognitive networks (Rogers al. 2007 Van
Den Heuvel & Pol 2010). This leads to complex correlations between fMRI time series of ROIs on brain, represented by functional connectivity.
Functional connectivity is formally defined as the temporal dependence of neuronal activity patterns of anatomically separated brain regions (Aertsen al., 1989. Fristoon et al.. 1993). Functional con- nectivity can be described through functional connectivity matrix (Venkatesh et al. 2020). whose elements indicate the strength of functional interactions between pairs of regions, with higher values signifying stronger correlations. This matrix reflects how different regions of the brain interact or communicate and is often used to study the brain's 's network organization and the functional relation- ships underlying cognitive and physiological processes.
Given that functional connectivity reflects the complex interactions between different brain regions, multi-level partitioning provides a powerful method to analyze these interactions across varying common approach in brain analysis, it allows for the simultaneous examination of brain behavior at both the macro level (e.g., interactions between brain regions) and the micro level (e.g., activity within local neuronal clusters) (Wang et al.) 2021 Kan et al.
spatial scales (Betzel & Basseti, 2017 Betzel al.) 2019). Multi-level partitioning
2023 Varga et al. (022), providing a more comprehensive understanding of brain function and structure across different spatial scales.
2.2 MULTIFRACTALITY OF FMRI SIGNALS.
The fractal behavior has been ubiquitously observed in neuroimaging studies which may arise from various mediators such as hemodynamics, respiration, cardiac fluctuations and brain neural activi- ties (Campbell & Weber (022). Extensive research has demonstrated that brain activity, regardless of the neuroimaging technique used for observation, is inherently arrhythmic and exhibits scale-free temporal dynamics (Racz al. 20188a Guan et al., (022). The scale invariance dynamics in fMRI is often associated with long- range correlation in time and has been extensively demonstrated in
numerous studies to be closely related intrinsic ongoing brain activity et al. 2014).
(Definition Scale-free law and Self-similarity) Data series generated by complex systems tend to fluctuate across different time scales (Boeing) 2016). These fluctuations often follow a scale-fres free law, maintaining consistent and invariant patterns across several orders of magnitude (Proekt et al.) 2012]. Scale-free dynamics can be described in the spectral domain by power law as the power spectrum follows a single power law over all ranges of frequency.
Let X denote the fMRI signals quantifying brain activity and [x()) is its Power Spectral Density (PSD). Scale-free property is classically defined (Ciuciu et al. 2012):
[x(() f
(1)
with f. power spectrum of fMRI data follows this power law across wide range of frequencies, suggesting that multiple frequencies equivalently contribute to its dynamics, rather than focusing solely on specific, preselected frequency band commonly used in brain analysis. Given that the fMRI signals X follow the power law described in equation I we further assume that ( is one miedimmntio time series data where is the time step and (() is a stationary jointly Gaussian process. Then the covariance function of Xt) can be expressed as follows: Cx(r) ox (1 ()), for
>> 1, where /3 is constant parameter known as scaling exponent. The
Tm I T I TM with a = 1 - 3. C' is a constant and o² is variance of X. Then it is easily to derive that; [X T) - X (t))
E. + 7)2 + EX (t)² 2EX (t+ x) (t) c - where 22 20x C". The fact that X is Gaussian further suggests that 4q > -1:
(t - x()) = c,l7|- 7 Tm < T S TM
(2)
Defining Y(t) = f (()dds. equation as follows, when Tm I T1, T2 S TM:
{
Y (1 + n - Y())
Y (1+++)) - Y())
(3)
TH
H
T2
SEER
Where H = (-a/2) = 1) and Idd means equality of all joint finite dimensional distributions. In other words, this means that for all q > -1, such that (t)( < xc:
E| Y()) c, 1 Tm S T S TM, or EJY (1+)) - EY Y()) [m 9
(4)
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when Tm T2 TM-
A geometric dataset exhibiting scale invariance is considered self-similar if it can be decomposed into smaller parts, each of which resembles the entire original structure (MIshra & Bhatnagar 2014).
As shown in equation 3 and equation
Y (t) is an example of a self-similar process.
From more generalized perspective, above equations not only fold for jointly Gaussian process but for a broader and more general class, that of self-similar processes with stationary increments, referred to as H-sssi processes, and defined in (Samorodnitsky al. 1996):
(X(1)EER fdd {a" (((a)))
(5)
For Va > 0, H E (0,1). Parameter H is referred to as the self-similarity exponent.
For real physiological data collected from brain, IMRI data can be also be viewed the increment process (t) = X (t 7o) - X (t) of an H-sssi process X, where To is a constant chosen by physi- ology and data acquisition set up, thereby exhibiting both scale-free and seff-similarity properties.
Data from H-sssi processes can be typically characterized by monofractal scaling exponents. How- ever, in reality, brain signals are more complex: while they exhibit global pattern consistency (monofractality). they also demonstrate distinct functional activity patterns in local areas (multifrac- tality) (Racz al., 2018b; França et al. 2018 La Rocca et al., 2018). This reflects the multi-scale regulation of neural activity in the brain. Larger-scale signals may capture whole-brain functional coordination, aligning with the global self-similarity described by monofractal models, whereas smaller-scale signals represent localized neuronal group activity.
(Definition Multifractality) For fMRI data (4). equation holds over a wide range of However, the scaling exponent deviate significantly from the expected linear behavior qH, manifesting
(6) Note the g-order scaling exponent ((q) is necessarily a strictly concave function of g. For this reason, instead of H-sssi process, there need broader class to depict this process, referred to as that of multifractal processes.
(1 + -) - (0) = c/17//19), -
Tm STS TM
Data with multifractal properties are more complex, featuring varying local characteristics and de- scribed by a range of scaling exponents. Multifractal signals exhibit both small-scale and large-scale local fluctuations, which are absent in monofractal signals. These fluctuations, associated with dif- ferent statistical moments, enable multifractals to capture fractal properties across multiple scales and represent localized nonlinear dynamics within the data (Lopes& & Betrouni 2009). By extending this capability, multifractal models provide a deeper understanding of brain dynamics, characteriz- ing the interactions across various scales and revealing how cognitive functions emerge from the synergy of processes operating at multiple levels.
3 METHOD
3.1 THE FRAMEWORK
The overall framework of the Physiological Dynamics-Driven Hierarchical Diffusion Model is il- lustrated in Figure D The fMRI time series data of subject with N ROIs can be denoted as
X, (Z1...... ".,...,,................. IN) Each z; spans T timesteps in the time series. We are given input data Xt, L:to, E R N where represents the size of the retrospective window, and ty denotes the initial position of the forecast window. The objective of the task is to predict the future fMRI values of N ROIs for a time span of t future time steps Xt E Nxt
Nx,, where 2; ETT represents the time series of the i-th ROL.
First, we input the fMRI time series data Xt, into the Hypergraph- based Hierarchical Signal Generator to produce R time series data XT,-L:10 where r denotes signals aggregated from r-level spatial ranges of brain regions. Then, we use a diffusion model to generate R time series data X7 Xi signals. Specifically, we first extract the historical embedding h; RNN, (x% h),-1) of the known time window using RNN, which serves as the basic historical condition Chistory for the diffusion process. This embedding is then input into the Dynamics Properties Guiding Module,
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Hicrarchical Feature Extracter
Crossbrain Region Guidling Progresiive Diflusion Medel
Mullsconditten Module
RNN
Xito
H
Multi condition
youd
Midule
ROI, Heady
Rio AMmm
ROI; wwweeeetieee
RNN
Multi condition
Medialo
ROL,
N
Nn
(a) HHSG: Hypergraph-losee Hierarchieal Signals Generator
(b) DPGM: Dynamics Propertios Guidligg Module
Multi-condtiin Module
My mmp
Besome Sumile uend
conitiie
Malifrracal Predicte
NLP
Hiiterial
HLP
DPGM
The framework of Physiological Dynamics-Driven Hierarchical Diffusion Model (PDH- Diffusion) with three main modules (a, b, and c), where we introduce two key physiological charac- teristics of brain fMRI to generate more realistic fMRI signals.
Figure 1:
where specifically designed loss function Lfractal is used to optimize the predicted multifrac- tal characteristies and generate the corresponding multifractal conditions Cfractal- Additionally, in the Cross-brain Region Guiding Progressive Diffusion Model, signals from broader brain region ranges X +t are used as cross-brain region conditions Cregion to guide the generation of more detailed signals Xi during the diffusion process. As a result, we obtain realistic generated signals Xt which accurately capture brain region relationships, fractal characteristics, while maintaining alignment with the known retrospective window data.
3.2 HYPERGRAPHI-BASED HIERARCHICAL SIGNALS GENERATOR
The first key module in our framework is the Hypergraph-basse based Hierarchical Signals Generator, where we model the complex interdependence between fMRI signals from sample points across dif- ferent brain regions as hypergraph structure. This structure enables the propagation of information across varying spatial scales of brain regions, resulting in hicrarchical fMRI signals that capture multiple levels information.
As mentioned before, the fMRI time series data of a subject with N ROIs is denoted X (.1)..., Fy ......... ,. x R- Traditional generation methods (Rasul et al. 2021 Alcaraz & Strodthoff, 2022) fail to capture the complex high-dimensional physiological and structural depen- dencies between IMRI data ROIs, leading to suboptimal outcomes. In this framework, we address this by modeling the relationships between IMRI signals from different ROIs using a hypergraph structure.
To align with real physiological conditions, we first model the fMRI signals as a standard graph structure Gs. based on the functional connectivity matrix C E N*N' as the adjacency matrix, where N is the number of ROIs and each element in C' reflects the interaction patterns between different ROIs (i.e., between distinct fMRI signals). In partieular, a threshold applied to the value distribution in C, where edges are established between sampling points that exhibit connectivity values exceeding the threshold. The resulting graph is denoted as G. = (V., Ea), where 0, E V, denotes vertex corresponding to sampling point, and ejj E &, represents edge connecting vertices i and Vy.
On the basis of constructed graph G. of fMRI signals, further construct hypergraph G (V, E, W) by defining hyperedges using the k-Hop neighbors method as described in (Gao et al. 2022 The hypergraph G consisting of vertex set V. a hyperedge set E, and hyperedge weight
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standard graph Ss
hypergraph G" with neighbor kr hypergraph G with neighbor k K++
The construction of hierarchical hypergraph. Starting from a standard graph G, constructed using rsFC as the adjacency matrix, hypergraphs with different aggregation levels G" are built using a k-hop method. As the number of neighbors k, increases, each node (fMRI signal of certain ROI) integrates more intra-regional and, gradually, inter-regional information (with different brain regions' information represented by different colors).
Figure 2:
matrix W and can be represented by its incidence matrix H E {0, 10 where the entries of
[1, if E We form hyperedge group using k-Hop neigh-
H are defined as: H(,,e) (0, otherwise.
bors & which seeks to identify vertices related to central node through k-Hop reachability within the graph and group them as hypervertex. The k-Hop neighborhoods of a vertex v in graph Go is defined as: Nhop, (v) = {u C # 0, u V.J. Here k can vary from [2, nel. where the number of vertices in G.. Finally, the hyperedge group with k-Hop can be written as: Enop, = ( (v) E Vl- Additionally, existing brain parcellation techniques can also be used to construct hypergraph Li et al. (2023), which may vary depending on the task performed dur- ing 1MRI acquisition. In the experiment, we select a neighbor list K {ki,..., kR). where each neighbor k,- is used to construct a corresponding hypergraph representing information from a distinct range of brain areas, shown in Figure 2
g". We construct R hypergraphs, each
In hypergraph propagation process, signal takes the aggregation of messages from its inter neighbor set vertices to get a new representation of the central vertex. We leverage the two steps of hypergraph message propagation method in (Gao al. 2022), which is defined two stage:
mg Σ Mx(xa)
mla Σ
Mc(Ho.Mo)
The first stage is:
(E...(
and the second stage is:
BENe(a)
V/ Un(W3, mz)
2/2 U.(Fa, m(a)
where Ta X is the signal of vertex V. and xY is the updated signal of vertex E V after information propagation. my is the message of hyperedge 3 E E and m', is the message of vertex a. Us the representation of hyperedge 3. M,(-), U.(.). M-(()),,(.). (-), U.() are the vertex message function, hyperedge update functions, hyperedge message function and vertex update function respectively. In experiment, we choose the basic implement as message function and update functions, both of which are mean functions and the propagation step is set to
By constructing IMRI data hypergraphs at various scales, we can obtain multiple sets of fMRI data X RR N XT FMRI data aggregated from larger regions capture broader brain area information, while data from smaller regions provide more detailed, localized insights within the region. To fully utilize these hierarchical fMRI signals and ensure complementary information across different brain regions, we design a cross-brain region guiding module, as detailed in Section 3.4
3.3 DYNAMICS PROPERTIES GUIDING MODULE
To ensure that the fMRI signals generated by the diffusion model exhibit the same dynamic charac- teristics as real brain physiological signals, we design module in which a multifractal properties predictor is optimized to estimate the multifractal characteristics of the signal over a future time window. The multifractal condition is then obtained through a projection layer and serves as one of the multiple conditions guiding the signal generation in the diffusion model.
We perform multifractal analysis on the fMRI signals and extract their fractal characteristics to serve ground truth. Multifractal detrended fluctuation analysis (MFDFA) is widely used method for analyzing the multifractal properties of time series, with detailed studies available in (Telesca et al. 2016 Ihlen 2012). This method provides various indicators to characterize the fractal nature of the

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time series. From these, we selected two representative and commonly used characteristics. Their descriptions are provided below:
1. The generalized Hurst exponent H (g): It reflects the inhomogeneity of the signal's structure. For monofractals, (g) is independent of the parameter q and remains constant, whereas for multifrac- tals, (q) varies with changes in q.
According to definition in Equation 6 (9) can be derived from the q-order scaling exponent ((q):
((q) = (g) Dr
where Dr is the topological dimension, which equals for time series.
2. The multifractal spectrum f(a): It implies the variation of the local Hurst exponent. The gener- alized fractal dimension (4)) and multifractal spectrum f(a) can be derived as:
((4) (()) = 9-1 a c'(())) f(a) = qa ((q)
(8)
Note that a and f(a) are also referred to as g-order singularity exponent hg and q-oreer singularity dimension Dy in (Thlen 2012), h and (h))n other literature (Thlen & Vereijken 2010).
Though the multifractal properties of fMRI time series can be calculated by MFDFA during the train- ing phase, in practical inference, no direct observations are available for the signals in future window. To address this, we design multifractal properties predictor to forecast the multifractal characteris- ties of future signals. The prediction is based on the historical embedding h RNN, (xf h)-1) which is extracted by RNN model from the observed window of the time series.
During training, we optimize the predicted generalized Hurst exponent H using the Mean Squared Error (MSE) loss, a commonly used loss function for regression tasks. Additionally, to ensure the predicted multifractal spectrum f(a) closely approximates the true distribution, we em- play the Kullback-Leibler (KL) divergence D (f (a))) to measure the difference between the predicted spectrum fax and the ground truth spectrum fa), which is calculated using MFDFA.
The complete fractal loss for a certain fMRI data x" is:
(r) D (1)
1 11 (Hi(g) H.(2))² + n.
Σ faa) -())))))))+++++++
log fi(a) f((a)
where n and the dimension of calculated generalized Hurst exponent and multifractal spectrum.
After obtaining the predicted multifractal properties, we project them using a multifractal projector, which can be implemented as MIP, and obtain the multifractal condition Cfractal that captures the multifractal dynamics of fMRI data.
3.4 CROSS-BRAIN REGION GUIDING PROGRESSIVE DIFFUSION MODEL.
We aggregate signals from brain regions of different ranges to complement the information in diffu- sion generation process, as signals from broader brain regions capture overall brain activity trends, while those from smaller regions provide finer details within a region. According to previous studies on brain function (Weiskopf et al. 2004 Kriegeskorte & Bandettini 2007), different brain regions respond to various tasks with distinct activation states, reflected in the overall increase or decrease trend of fMRI signals. diffusion model, the broader trend signals correspond the early genera- tion steps, representing brain region activity larger scale. Therefore, we generate fMRI signals that represent the general activity trends of broader brain regions, and then use these trends as con- ditions to guide the generation of finer-scale signals. This multi-level, progressive approach ensures that signals at each level collectively contribute to refining the generation of the final fMRI signal.
Intuitively, the signal representing the trend across broader range of brain regions tends to be smoother, as it integrates multiple fMRI signals that exhibit similar trends within that region. As a re- sult, fewer diffusion generation steps required. We also up share ratio in (Fan al. 2024), defined as: o, := (N, 1)/N, which represents the shared percentage of variance schedule between the data aggregated from rleeel brain region and the original data. For the original fMRI
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data, N, = 1 and 01
0f (N:) -
if I...., NT. if No + +1,..,
(10)
Here, {37) {1- a J n=1 the variance schedule diffusion and a (NI) by (NT) = I o (MI). Noted that aligning with the intuition, there is N < N N No for brain region level r E {1,...,f...
II of
Unlike the conventional multi-granularity diffusion generation process, in the case of brain fMRI generation, signals representing different spatial scales of brain regions play clearer guiding role. We first generate signals that represent the overall active trend brain regions, which then guide the generation of finer detailed signals within each region. To achieve this, we establish a progressive generation framework. Specifically, when generating the signal at the r-th level, we leverage (r+1), th level generated signal through extracting its embedding and then mapping it by MLP, cross-brain region condition Cregion to guide the diffusion generation.
3.5 TRAINING PROCEDURE
For the signal aggregated from r-range of brain regions, train the conditional denoising diffusion model with condition c" = WhChistory + w wjCfrectol + Cregioon We have diffusion loss ( (6) at timestep / and diffusion step as below, where E ~ N/0, I):
di fusion (0) E, II(E - E6( =6( ab. + (b,,nn,c"))
(11)
The final training objective is a weighted sum of diffusion loss in Equation and the fractal loss in Equation 9 for all signals:
L funal
Σ
w L
fussiononn (0)
Σ L
fractal (7)
(r)
(12)
R
Σ w Be [||c co(2%) n, cn)
Σ
L fractal (7),
where That a / by and ER : 1 is hyper-parameter controlling the scale of
guidance as (Fan et al. 2024
EXPERIMENT
4.1 SETTINGS
Datasets
To evaluate the advanced capabilities of proposed fMRI generation method, choose the Human Connectome Project (HCP) dataset 900 Subject Release (Van Essen et al. 2012; 2013), which is public fMRI dataset for brain related research. We preprocess the fMRI data using standard meth- ods (Glasser et al., 2013) and parcellate it into nodes using a whole-brain functional AAL atlas, from which we select 86 nodes in the cerebrum. The brain functional connectivity matrix constructed by calculating the Pearson correlation between the fMRI time series of different brain ROIs.
Baselines and Evaluation Metrics
As our model is diffusion-based time series generation model, we mainly choose two types of base- lines compare. (1) we choose time series forecasting methods, such as TimesNet (Wu al. 2023).
Flowformer (Huang et al., 2022). iTransformer (Liu et al.) 2023), MSGNet (Cai et al. 2024). U- Mixer (Ma et al.) 2024); (2) we include recent time series diffusion models: non-autoregressive dif-
fusion model Trad (Rasul et al. 202T), structured state space model-based diffusion SSSD (Al-
caraz & Strodthoff 2022).
We evaluate model and all baselines using MAE (Mean Absolute Error), MAPE (Mean Absolute Percentage Error) and RMSE (Root Mean Square Error), which are widely used metries for accuracy of time series forecasting.
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Figure 3: Prediction performance of fMRI signals across 32 and 96 time steps. Each row represents different subject, and each column corresponds to distinct ROI.
Table I:
Comparison on IMRI forecasting task on HCP dataset. Baseline methods include time series forcasting methods (TimesNet (Wu al.) (202), Flowformer (Huang al., 2022). iTrans-
former (Liu et al. 2023). MSGNet (Cai et al.) 2024). U-Mixer (Ma et al. (022)) ) and the diffusion-
based method (TimeGrad (Rasul et al. 2021), SSSD (Alcaraz & Strodthoff 2022 + indicates
smaller values are preferred. Bold font indicates the best result in a column.
Method
Tyred 32
MAPE(S))
MAE
Taral 61 MAPE(S)
MAE
RMSK
Tind 96
TimesNet et 2023
31.17
42.12
0.2956
31.39
42.64
0.2998
31.70
42.82
0,3015
Flowformer Hunse ct 3 2022
30.55
40.89
0.2917
30.74
40.16
0.2953
30.97
40.28
0.2974
iTunsformer
32.64
43.54
0,3166
32.52
43.59
0,3183
32:77
43.82
0.3214
31.21
42,90
U-Mixer or
2024
29.36
39.70
0.2793
29:42
39.81
0.2804
29.83
39.92
0.2817
TimeCindd Raail et al. 1r
34.47
47.79
0.3413
36.42
49.13
0.3527
37.62
$0.35
0,3720
Akkara Stroillsol1
34.38
PDA-Diffusion (Ouns)
28.56
38.70
0.2744
29.04
38.91
0.2768
29.73
39.25
0.2803
Experimental Setups
There are 696 data in training dataset and 174 data in test dataset. Each data has size NROT x T. where RoOr 82 is the number of ROIs on brain, T = 1200 is the timesteps of fMRI time series. For fMRI time series prediction, we set the context length L 64, and prediction length Tpred = {32, 64, 96]. These settings were applied to all compared models. The imitial learning rate was LR = 0.00001 and batch size was 32. The training was conducted for 200 epochs.
4.2 RESULTS AND ANALYSIS
The MAE, RMSE, and MAPE values, averaged over 10 independent runs, are reported in Table From the results, we can see for all three prediction time length Tpred 32, T Tpred 64 and Tpred = 96, PDH-Diffusion consistently outperforms the baselines in terms of MAE, RMSE, and MAPE. We also observe that as the prediction length increases while keeping the context length constant, the forcasting accuracy of all models declines to varying degrees. We show the prediciton performance of fMRI data in Figure 3 Overall, the result indicates that our method can generate fMRI that are closest to the true physiological fMRI signals.
4.3 ABLATION ANALYSIS
To verify the rational business of our framework, we provide detailed ablations. In particularly. we conducted three separate ablation experiments, each corresponding to the removal of one of the proposed modules: (1)w/o-HHSG, i.c. Model without the Hypergraph- basedd Hierarchical Signals Generator from the framework, meaning that the diffusion model was only trained to generate the original fMRI data without any cross-brain region information. (2)/o-DPGM, i.e. Model with- out the Dynamics Properties Guiding Module, which also eliminates the need for the loss function L Lfractal during training. (3)w/o-CRGM. i.e. Model with the Cross-brain Region Guiding Progres- sive Diffusion Model removed, which means there is no cross-brain region condition derived from the wider range of brain regions. We evaluated the whole framework with these three variants HCP dataset and the results are reported in Table highlighting improvements of proposed modules.
The influence of the weights of condition Cfractat and Cregion
In the proposed framework, the diffusion generation process is guided by multiple conditions, with the historical condition as the base and the cross-brain region and multifractal conditions added.

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Published as a conference paper at ICLR 2025
Table 2:
Ablation study covering removing three key components proposed in framework.
Table 3: The influence of the brain region range setting in HHSG.
Metric
MAE
RMSE
MAPE (S))
Number of ranges
MAE 1
RMSE 4
MAPE(S) J
PDH-Dimusioufull)
29.04
38.91
0.2768
34.26
44.93
0.3397
33.89
44.25
0,3314
Woo-IIISG
34.26
44.93
0.3397
wo-DPGM
29.86
40.24
0.28933
w/-CRGM
31.08
42.47
0.3218
To evaluate the importance of these additional conditions, explored the impact of their weights Wr and wy on the generation results, as presented in Figure 4a
As shown in Figure 4a for both conditions, the results initially decrease and then increase as the weight grows The initial decline reflects the effectiveness of the added conditions, while the sub- sequent increase may be due excessive weighting interfering with the basic (history) condition. Additionally, it demonstrates that the fractal condition consistently improves the generation results.
MAE
MAE
50.0
tringh tra Suggen
40.0
30.0
Weight region (w.) Weight multfractallly (w)
20.0
(a) The impact of the weights of cross-brain region condition and multifractal condition.
(b) The influence share ratios on the generation of signals from different brain ranges.
Figure 4: The impact of weights of conditions and share ratios.
The influence of share ratios o
To assess the impact of the share ratios a signal generation across different brain region ranges, we conducted an experiment with four ranges (R 4), as shown Figure 4b] The share ratio for signal from each range was varied from 0.1 to 1. In the figure, = 1 represents the original, most localized signal, while = corresponds to the signal from the widest brain region range.
Figure shows that for the original signal, which contains more detailed local information, a higher share ratio leads to better generation performance. contrast, for signals that aggregate more global information and represent broader brain region trends, the optimal share ratio tends to be lower.
The influence of brain region range setting
In Table 3 we experimentally examined the effect of varying the number of ranges of brain regions on the generated results. As shown in Table the generation performance improves the number of ranges of brain regions increases, indicating that richer and more detailed transmission of brain region information significantly enhances the quality of generated IMRI signals. This finding further suggests that incorporating additional medical- based prior knowledge about brain partitions holds great potential for further improving fMRI signal generation.
CONCLUSION
this paper, we propose the Physiological Dynamics-Driven Hierarchical Brain Diffusion Model, novel framework for generating realistic fMRI time series by integrating key aspects of brain functional connectivity and multifractal dynamics. By leveraging a hypergraph- baased functional connectivity structure and multifractal guiding module, approach improves the physiological accuracy of generated fMRI signals, addressing limitations in current generative models and offering potential for enhanced applications in neuroscience and clinical diagnosis.
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Published as a conference paper at ICLR 2025
6 ACKNOWLEDGMENTS
This work was supported by Hong Kong Research Grants Council (RGC) General Research Fund 14220622 and CUHK 4055188.
REFERENCES
AM Aertsen, GL Gerstein, MK Habib, and GwtcoPGK Palm. Dynamics of neuronal firing correla- tion: modulation of"" effective connectivity". Journal of neurophysiology, 61(5)9000-917, 1989.
Juan Miguel Lopez. Alcaraz and Nils Strodthoff. Diffusion-based time series imputation and fore- casting with structured state space models, arXiv preprint arXiv:2208.09:3 2022.
Joshua A Bagley, Daniel Reumann, Shan Bian, Julie Lévi-Strauss, and Juergen A Knoblich. Fused cerebral organoids model interactions between brain regions. Nature methods, 14(7):743-751, 2017.
Richard F Betzel and Danielle S Bassett. Multi-scale brain networks. Neuroimage, 160:73-83, 2017.
Richard Betzel, Maxwell A Bertolero, Evan M Gordon, Caterina Gratton, Nico UF Dosenbach, and Danielle S Bassett. The community structure of functional brain networks exhibits scale- specific patterns of inter-and intra-subject variability. Neuroimage, 202: 15990, 2019.
Geoff Boeing. Visual analysis of nonlinear dynamical systems: chaos, fractals, self-similarity and the limits of prediction. Systems, 4(4):37, 2016.
Saskia Bollmann and Markus Barth. New acquisition techniques and their prospects for the achiev- able resolution of fmri. Progress in neurobiology, 207:101936, 2021.
Wanlin Cai, Yuxuan Liang, Xianggen Liu, Jianshuai Feng. and Yuankai Wu. Msgnet: Learning multi-scale inter-series correlations for multivariate time series forecasting, In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 11141-11149, 2024.
Olivia Lauren Campbell and Alexander Mark Weber. Monofractal analysis of functional magnetic resonance imaging: An introductory review. Human Bruin Mapping, 43(8):2693-2700 2022.
Philippe Ciuciu, Gaäl Varoquaux, Patrice Abry. Sepideh Sadaghiani, and Andreas Kleinschmidt. Scale-free and multifractal time dynamics of fmri signals during rest and task. Frontiers in phys- iology, 3:186 16, 2012.
Philippe Ciuciu, Patrice Abry, and Biyu J He. Interplay between functional connectivity and scale- free dynamics in intrinsic fmri networks. Neuroimage, 95:248-263, 2014.
Mark D'Esposito, Leon Y Deouell, and Adam Gazzaley. Alterations in the bold fmri signal with ageing and disease: a challenge for neuroimaging. Nature Reviews Neuroscience, (11):863-877) 2003.
Xinyao Fan, Yucying Wu, Chang Xu, Yuhao Huang, Weiqing Liu, and Jiang Bian. Mg-tsd: Multi-granularity time series diffusion models with guided learning process. arXiv preprint arXiv:2403.05751, 2024.
Lucas G Souza França, José G Vivas Miranda, Marco Leite, Niraj K Sharma, Matthew C Walker, Louis Lemieux, and Yujiang Wang. Fractal and multifractal properties of electrographic record- ings of human brain activity: toward its use as a signal feature for machine learning in clinical applications. Frontiers in physiology, 9:1767, 2018
Karl Friston, Chris D Frith, Peter Liddle, and Richard SJ Frackowiak. Functional connectivity: the principal-comppnentt analysis of large (pet) data sets. Journal of Cerebral Blood Flow & Metabolism, 13(1)55-14, 1993.
Yue Gao, Yifan Feng, Shuyi Ji, and Rongrong Ji. Hgnn+: General hypergraph neural networks. IEEE Transactions Pattern Analysis and Machine Intelligence, 45()):311-3119, 2022.
11

---

Published as a conference paper at ICLR 2025
Matthew F Glasser, Stamatios N Sotiropoulos, J Anthony Wilson, Timothy S Coalson, Bruce Fischl, Jesper Andersson, Junqian Xu, Saad Jbabdi, Matthew Webster, Jonathan R Polimeni, et al. The minimal preprocessing pipelines for the human connectome project. Neuroimage, 80:105-124, 2013.
Sihai Guan, Dongyu Wan, Yanmiao Yang, and Bharat Biswal. Sources of multifractality of the brain r8- rs-fmri signal. Chaos, Solitons & Fractals, 160:1 12222, 2022.
Biyu J He. Scale-free brain activity: past, present, and future. Trends in cognitive sciences, 18(9): 4800487, 2014.
Zhibin He, Wuyang Li, Tuo Zhang, and Yixuan Yuan. H gm: A hierarchical hypergraph matching framework for brain landmark alignment. In MICCAI, pp. 548 158-558,44 2023.
Zhibin He, Wuyang Li, Yu Jiang, Zhihao Peng, Pengyu Wang, Xiang Li, Tianming Liu, Junwei Han, Tuo Zhang, and Yixuan Yuan. F2tnet: Fmri to tlw mri knowledge transfer network for brain multi-phenotype prediction. In MICCAI, 2024.
Zhaoyang Huang, Xiaoyu Shi, Chao Zhang, Qiang Wang, Ka Chun Cheung. Hongwei Qin, Jifeng Dai, and Hongsheng Li. Flowformer: transformer architecture for optical flow. In European conference on computer vision, pp. 668-685. Springer, 2022.
Espen AF Ihlen. Introduction multifractal detrended fluctuation analysis in matlab. Frontiers in physiology, 3:141, 2012.
Espen AF Ihlen and Beatrix Vereijken. Interaction Interaction-dominant dominant dynamics in human cognition: Beyond
1/fa fluctuation. Journal of Experimental Psychology: General, 139(3):436, 2010.
Xuan Kan, Antonio Aodong Chen Gu, Hejie Cui, Ying Guo, and Carl Yang. Dynamic brain trans- former with multi-level attention for functional brain network analysis. In 2023 IEEE EMBS International Conference Biomedical and Health Informatics (BHI), pp. 1-4. IEEE, 2023.
Nikolaus Kriegeskorte and Peter Bandettini. Analyzing for information, not activation, to exploit high-resolution fmri. Neuroimage, 38(4):649 6621666,.66666.. 2007.
Daria La Rocca, Nicolas Zilber, Patrice Abry. Virginie van Wassenhove, and Philippe Ciuciu. Self- similarity and multifractality in human brain activity: A waselet-based analysis of scale-free brain dynamics. Journal of neuroscience methods, 309: 175-177, 2018.
Chenxin Li, Hengyu Liu, Yifan Liu, Brandon Feng, Wuyang Li, Xinyu Liu, Zhen Chen, Jing Shao, and Yixuan Yuan. Endora: Video generation models as endoscopy simulators. In MICCAI, pp. 230-240, 2024a.
Wuyang Li, Xinyu Liu, and Yixuan Yuan. Sigma++: Improved semantic- compltec graph matching for domain adaptive object detection. TPAMI, 45(7):902--9000, 2023.
Wuyang Li, Xinyu Liu, Jiayi Ma, and Yixuan Yuan. Cliff: Continual latent diffusion for open- vocabulary object detection. In ECCV, pp. 255-273. 2024b.
Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. itransformer: Inverted transformers effective for time series forecasting. arXiv preprint arXiv:2310.06625, 2023.
Nikos K Logothetis. What we can do and what we cannot do with finri. Nature, 453(7197):869--77) 2008.
Renaud Lopes and Nacim Betrouni. Fractal and multifractal analysis: review. Medical image analysis, 13(4):634-64) 649, 2009.
Xiang Ma. Xuemei Li, Lexin Fang, Tianlong Zhao, and Caiming Zhang. U-mixer: An unet-mixer architecture with stationarity correction for time series forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 14255-14262 2024.
Paul M Matthews, Garry D Honey, and Edward T Bullmore. Applications of fmri in translational medicine and clinical practice. Nature Reviews Neuroscience, 7(9):332-744, 2006.
12

---

Published as a conference paper at ICLR 2025
Voichija Maxim, Levent Sendur, Jalal Fadili, John Suckling, Rebecca Gould, Rob Howard, and Bullmore. Fractional gaussian noise, functional mri and alzheimer's disease. Neuroinage, 25 (1):141-158, 2005.
Punya MIshra and Gaurav Bhatnagar. seif-similarity. Ar Right Angles, 3(2):23-33) 2014.
Jonathan D Power, Anish Mitra, Timothy O Laumann, Abraham Z Snyder, Bradley L Schlaggar, and Steven E Petersen. Methods to detect, characterize, and remove motion artifact in resting state fmri Neuroimage, 84:320-341, 2014.
Alex Proekt, Jayanth R Banavar, Amos Maritan, and Donald W Pfaff. Scale invariance in the dynamics of spontaneous behavior. Proceedings of the National Academy of Sciences, 109(26): 10564-10569, 2012.
Frigyes Samuel Racz, Peter Mukli, Zoltan Nagy, and Andras Eke. Multifractal dynamics of resting- state functional connectivity in the prefrontal cortex. Physiological measurement, 39(2):220033, 2018a.
Frigyes Samuel Racz, Orestis Stylianou, Peter Mukli, and Andras Fke. Multifractal dynamic func- tional connectivity in the resting-state brain. Frontiers Physiology, 9:1704, 2018b.
Kashif Rasul, Calvin Seward, Ingmar Schuster, and Roland Vollgraf. Autoregressive denoising dif- fusion models for multivariate probabilistic time series forecasting. International Conference on Machine Learning, pp. 8857-8868. PMLR, 2021.
Baxter P Rogers, Victoria L Morgan, Allen T Newton, and John Gore. Assessing functional connectivity in the human brain by fmri. Magnetic resonance imaging, 25(10))1347-1337, 2007.
Gennady Samorodnitsky, Murad Taqqu, and RW Linde. Stable non-gaussian random processes: stochastic models with infinite variance. Bulletin of the London Mathematical Society, 28(134): 554 555, 1996.
Lifeng Shen, Weiyu Chen, and James Kwok. Multirresolution diffusion models for time series forecasting. In The Twelfth International Conference on Learning Representations, 2024.
Gary Strangman, David A Boas, and Jeffrey P Sutton. Non-invasive neuroimaging using near- infrared light. Biological psychiatry, 52(7):679-66) 693,, 2002.
John Suckling, Alle Meije Wink, Frederic A Bernard, Anna Barnes, and Edward Bullmore. En- dogenous multifractal brain dynamics are modulated by age, cholinergic blockade and cognitive performance. Journal of neuroscience methods, 174(2):292-300 2008.
Enzo Tagliazucchi, Frederic von Wegner, Astrid Morzelewski, Verena Brodbeck, Kolja Jahnke, and Helmut Laufs. Breakdown of long-range temporal dependence in default mode and attention networks during deep sleep. Proceedings of the National Academy of Sciences, 110(38):1541-- 15424, 2013.
Luciano Telesca, Michele Lovallo, and Mikhail Kanevski. Power spectrum and multifractal de- trended fluctuation analysis of high-frequency wind measurements in mountainous regions. Ap- plied energy, 162:1052-1061, 2016.
Martijn P Van Den Heuvel and Hilleke E Hulshoff Pol. Exploring the brain network: a review on resting-state fmri functional connectivity. European neurapschhppharmccooyyy 2095)35 2010.
David C Van Essen, Kamil Ugurbil, Edward Auerbach, Deanna Barch, Timothy EJ Behrens, Richard Bucholz, Acer Chang. Liyong Chen, Maurizio Corbetta, Sandra W Curtiss, et al. The human connectome project: data acquisition perspective. Neuroimage, 62(4)) 2231, 2012.
David C Van Essen, Stephen M Smith, Deanna M Barch, Timothy EJ Behrens, Essa Yacoub, Kamil Ugurbil, Wu-Minn HCP Consortium, et al. The wu-minn human connectome project: overview. Neuroimage, 80:62-79, 2013.
13

---

Published as a conference paper at ICLR 2025
Levente Varga. Vasile V Moca, Botond Molnár, Laura Perez-Cervers Mohamed Kotb Selim, Anto- nio Diaz-Parra, David Moratal, Balázs Péntek, Wolfgang H Sommer, Raul C Muresan, al. Brain dynamics supported by hierarchy of complex correlation patterss defining robust functional architecture. Cell Systems, 1588)7770-786 2024.
Manasij Venkatesh, Joseph Jaja, and Luiz Pessoa. Comparing functional connectivity matrices: A geometry-aware approach applied participant identification. Neurolmage, 207:116398, 2020.
Rong Wang. Mianxin Liu, Xinhong Cheng, Ying Wu, Andrea Hildebrandt, and Changsong Zhou. Segregation, integration, and balance of large-scale resting brain networks configure different cognitive abilities. Proceedings of the Nutional Academy of Sciences, 118(23))e20222881 18, 2021.
Nikolaus Weiskopf, Frank Scharnowski, Ralf Veit, Rainer Goebel, Niels Birbaumer, and Klaus Mathiak. Self-regulation of local brain activity using real-time functional magnetic resonance imaging (fmri). Journal of Physiology-Paric 98(4-6):357-373, 2004.
Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang. and Mingsheng Long- Timesnet: Temporal 2d-variation modeling for general time series analysis. In International Conference on Learning Reprexentations, 2023.
14


Reviews:
[{"review_id": "bSJFLKD8Nv", "reviewer": "Reviewer_wJoL", "summary": "This paper proposes a novel approach for generating realistic fMRI data using diffusion models, specifically designed to account for regional interactions and spectral features of the brain. The model captures regional connectivity in a hierarchical structure, where fine-scale signals are conditioned on larger-scale signals. To learn spectral features, it incorporates loss functions that capture fractal characteristics. Results demonstrate improved performance over existing time-series forecasting and diffusion-based models. Additionally, ablation studies validate the effectiveness of each model component.", "questions": "1. What is the sampling frequency for the fMRI?\n2. It would be beneficial to analyze the reconstructed signal to determine if the observed patterns align with expectations. Calculating the spectrum and fractal characteristics would provide an important validation of the model’s effectiveness. Additionally, some neurological features can also be checked. For instance, if the data is from resting-state fMRI, does it reveal the default mode network?  \n3. Line 465 typo 69->96", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The proposed method, which captures connectivity and spectral features, is a novel approach. \n2. The method is rigorously validated using multiple benchmarks and ablation studies.", "weaknesses": "1. The paper has limited reproducibility due to missing details about data preparation and experimental setup. Additional information is needed on the dataset used, including whether it involved resting-state or task-based fMRI, whether subjects were healthy or under specific conditions, and the rationale for selecting regions of interest (ROI), which were reduced from 268 to 82. Clarification on data split (e.g., train/test division, sample counts) is also required. If the codebase will not be provided, the paper should include a detailed description of the network architecture (such as layer specifications and activation functions) and the training setup for benchmark methods in an appendix.\n2. The practical implications, particularly the clinical applications of the proposed method, are somewhat unclear and could benefit from further exploration and discussion.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jNTa2g26Iu", "reviewer": "Reviewer_hv4T", "summary": "In this paper, the authors proposed a novel framework named the Physiological Dynamics-Driven Hierarchical Diffusion Model (PDH-Diffusion) for fMRI analytics. The PDH-Diffusion framework integrates two essential brain physiological properties, hierarchical regional interactions and multifractal dynamics, into the diffusion process. The primary goal is to improve diffusion models’ capability to generate realistic fMRI time series signals by accurately capturing these physiological characteristics.", "questions": "The reviewers have raised several questions regarding the weaknesses of this work:\n\n1). Qualitative Comparisons: The authors are strongly encouraged to provide qualitative comparisons between the synthesized and real fMRI signals to allow for a qualitative assessment of the model’s performance.\n\n2). Optimal Range of Brain Regions: The results suggest an “optimal” range of brain regions that enhances performance. How is this range determined, and is it manually set? Reviewers are concerned about the reliance on manual design for determining this optimal range.\n\n3). Validation of Multifractal Properties: How do the authors validate that the generated signals preserve multifractal properties?\n\n4). Risk of Overfitting: Do the variance schedule parameters ($\\alpha_n$ and $\\beta_n$) and the historical data used in training the PDH-Diffusion model lead to overfitting?", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "Overall, the major strength of this work lies in its novelty. The authors have developed an innovative framework that captures complex interdependencies and multifractal dynamics within synthetic fMRI signals.\n\nSpecifically, their contribution includes integrating three key components into the diffusion process: a hypergraph-based signal generator, a dynamics properties guiding module, and a cross-brain region progressive diffusion model. This integration enhances the realism of the generated signals. The authors provide a robust theoretical foundation for their methods and perform extensive quantitative analysis, demonstrating the framework’s accuracy and effectiveness in time series forecasting. The paper is well-organized and includes relevant background information. Results from the proposed method outperform multiple peer models in time-series forecasting and diffusion models, as evidenced by superior MAE, MAPE, and RMSE scores, highlighting the model’s effectiveness.", "weaknesses": "The reviewers have multiple concerns about the framework and potential impact in this work. \n\n1). The confusion about physiological fMRI. Usually, fMRI are categorized into resting-state and task-based fMRI. The resting-state fMRI is commonly scanned without specific stimulus, whereas task-based fMRI is acquired based on external stimulus, such as 7 tasks in HCP. Is physiological fMRI is either resting-state or task-based signal? The authors do not clarify the concept even in Introdcution section.\n\n2). Limited motivation and impact. In Abstract, the authors mentioned \"Functional magnetic resonance imaging (fMRI) is essential for mapping brain activity but faces challenges like lengthy acquisition time and sensitivity to patient movement, limiting its clinical and machine learning applications.\" It seems that the authros' work can advance the fMRI for clincial application, but the authors do not generate some neurological or psychiatric fMRI to validate. From reviewers' perspective, using the innovative PDH-Diffusion model, it can assist physician to provide lengthy fMRI signal which will denfinitely reduce the inconvenience of patients. Only generating healthy fMRI can impair the motivation and impact of this work.\n\n3). Lacking of qualitative comparison. The authors have provided an extensive quantitative validation of PDH-Diffusion model with other peer methods using MAE, MAPE, and RMSE. Unfortunately, the autors do not provide any qualitative results, such as Functional Connectivity Map or Brain Connectivity Maps, of PDH-Diffusion. That is, although averaging metrics such as MAE, RMSE, MAPE across 10 runs may demonstrate robustness, these metrics  cannot fully capture the quality or realism of the synthesized fMRI signals. Notably, the qualitative results is also vital in clinics, since these results showcase which brain regions are severly impaired by neurological disorders.  Importantly, there is no visual representation given of the generated fMRI signal, which would be valuable for assessing their plausibility. \n\n4). Several technical issues. The variance schedule (parameters $\\alpha_n$ and $\\beta_n$) in the diffusion process may not be fully optimized for different regions or scales, potentially leading to inappropriate noise levels in certain hierarchical levels. This could result in over-smoothing or overfitting at certain levels. Additionally, conditioning on historical data could lead to overfitting if the model becomes too dependent on past values, especially if the training data does not represent the full spectrum of brain dynamics. Without explicit mitigation measures, such as adaptive variance schedules or regularization techniques, these issues may limit the model’s ability to generalize to new or varied patterns, impacting its robustness and effectiveness.\n\n5). Multiple typographical mistakes. In Section 4.3 (ABLATION ANALYSIS) there are many typographical errors. The term “share radio” is used instead of ‘share ratio’ in “The influence of share radio” this section. Similar typographical errors appear in the caption and text of Figure 3(b), as well as in Section 3.4. These typographical mistakes impair the redability of this paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hfEXxs0g2S", "reviewer": "Reviewer_fBZF", "summary": "This paper proposes 'PDH-Diffusion', a framework that synthesizes fMRI data through a hypergraph-based hierarchical signals generator, the properties of a dynamic guiding module, and a cross-brain region guiding progressive diffusion model. The authors first introduced scientific priors, motivation, and concrete realization for building these modules in detail. They then provided the quantified results compared with previous approaches and the ablation experiment, showing their architecture has better performance in generating fMRI than other baseline models.", "questions": "1. As noted in the weaknesses, synthetic neural signals are particularly intriguing in the neuroscience field. Would this framework be adaptable for application or testing on other fMRI datasets, especially those with different clinical populations, to assess its generalizability? \n\n2. Typically, fMRI signals are recorded in a low temporal resolution. Could the model be extended to work with high temporal resolution modalities, such as magnetoencephalography (MEG) or electroencephalography (EEG), where realistic signal synthesis could enhance downstream analyses?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "1. The paper established a novel framework for fMRI synthesis taking the dynamic characteristics and structure of the brain into consideration which has the solid and strong theoretical support.\n2. The model incorporates hierarchical brain regional interactions and multifractal dynamics, enabling it to generate fMRI signals that better reflect physiological properties.", "weaknesses": "1. In the ''Experimental Setups'' section, the experiment did not test on multiple fMRI datasets or finer parcellation atlas, but only used the HCP dataset on the AAL atlas, which makes the results of the experiment not that solid. Meanwhile, I would suggest the framework could be extended to and tested in other modalities, for instance, EEG signals.\n2. Although the paper introduces a novel framework for generating fMRI data, it lacks validation on the generated data’s impact on downstream tasks, such as disease diagnosis, or brain network analysis.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Y1LVx31nsF", "reviewer": "Reviewer_ouRH", "summary": "In this study, the authors proposed a novel algorithm for synthesizing realistic functional MRI (fMRI) via physiological dynamics-driven hierarchical diffusion model. Then, the authors validated the feasibility of synthesized fMRI data by comparing it to other generative mechanisms. The scientific merit of this work mainly comes from the conceptual advances in their proposed algorithm. It is indeed challenging to synthesize realistic fMRI data while preserving unique aspects of the brain system. The authors combined three different modules, each serving different roles, to synthesize brain dynamics with preserved network-like structure and fractal components. Given results of the extensive validation experiment on the large fMRI cohort, the validity of the proposed algorithm is clear; yet, the scientific significance of this work is somewhat limited as there was no experiment demonstrating the practical usefulness of the proposed algorithm.", "questions": "1. In table 1, does “T_Pred=32 or 64” mean predicting 32 or 64 time points of fMRI data?\n2. If my speculation in the former question is right, it is counter-intuitive that forecasting more time points (96 vs. 32) did not lead to an increase in errors. Please clarify this. \n3. According to Fig 1, it looks like the resolution of synthesized data is bounded to the level of ROI. It is more desirable to synthesize fMRI dynamics at the level of vertex. Is the proposed method able to be applied at the vertex level as well?     \n4. In line 451, please double check the definition of MAE.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The major originality of this study comes from its conceptual advances embedded in the proposed algorithm. It is indeed challenging to synthesize realistic fMRI data while preserving unique aspects of the brain system. The quality and clarity of the models in the main text are reasonably strong as well.", "weaknesses": "The major concern comes from the unclear significance of this work. As the authors argued in the Introduction, acquisition of fMRI is expensive. Thus, synthesizing fMRI signal can be tempting. Although expensive, real fMRI data reflects unique information of individuals. This study, however, was not able to demonstrate the synthesized fMRI still convey unique information of subjects. Slight improvement in forecasting future timepoints of fMRI signal does not suggest the significance or practical usefulness of the model. This works needs additional analysis or applications highlighting the unique advantage of the synthesized fMRI data from the proposed model.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)