Conditional Diffusion with Ordinal Regression: Longitudinal Data Generation for Neurodegenerative Disease Studies
Authors: Hyuna Cho
Ziquan Wei
Seungjoo Lee
Tingting Dan
Guorong Wu
Won Hwa Kim
Venue: ICLR 2025 Spotlight (2025)
Keywords: neurodegenerative disease
conditional diffusion model
longitudinal data analysis
Primary area: applications to neuroscience & cognitive science

Abstract: Modeling the progression of neurodegenerative diseases such as Alzheimer’s disease (AD) is crucial for early detection and prevention given their irreversible nature. However, the scarcity of longitudinal data and complex disease dynamics make the analysis highly challenging. Moreover, longitudinal samples often contain irregular and large intervals between subject visits, which underscore the necessity for advanced data generation techniques that can accurately simulate disease progression over time. In this regime, we propose a novel conditional generative model for synthesizing longitudinal sequences and present its application to neurodegenerative disease data generation conditioned on multiple time-dependent ordinal factors, such as age and disease severity. Our method sequentially generates continuous data by bridging gaps between sparse data points with a diffusion model, ensuring a realistic representation of disease progression. The synthetic data are curated to integrate both cohort-level and individual-specific characteristics, where the cohort-level representations are modeled with an ordinal regression to capture longitudinally monotonic behavior. Extensive experiments on four AD biomarkers validate the superiority of our method over nine baseline approaches, highlighting its potential to be applied to a variety of longitudinal data generation.

Published as a conference paper at ICLR 2025
CONDITIONAL DIFFUSION WITH ORDINAL REGRES- SION: LONGITUDINAL DATA GENERATION FOR NEURODEGENERATIV DISEASE STUDIES
Hyuna Cho', Ziquan Seungjoo Lee', Tingting Dan", Guorong Wu², Won Hwa Kim POSTECH,, South Korea
University of North Carolina at Chapel Hill, USA
ABSTRACT
Modeling the progression of neurodegenerative diseases such as Alzheimer's dis- ease (AD) is crucial for early detection and prevention given their irreversible na- ture. However, scarcity of longitudinal data and complex disease dynamics make the analysis highly challenging. Moreover, longitudinal samples often contain irregular and large intervals between subject visits, which underscore the neces- sity for advanced data generation techniques that can accurately simulate disease progression over time. In this regime, we propose novel conditional generative model for synthesizing longitudinal sequences and present its application to neu- rodegenerative disease data generation conditioned on multiple time-dependent ordinal factors, such as age and disease severity. Our method sequentially gener- ates continuous data by bridging gaps between sparse data points with diffusion model, ensuring a realistic representation of disease progression. The synthetic data are curated integrate both cohort-level and individual-specift characteris- tics, where the cohort-level representations are modeled with an ordinal regression capture longitudinally monotonic behavior. Extensive experiments biomarkers validate the superiority of our method over nine baseline approaches, highlighting its potential be applied to variety of longitudinal data generation.
four AD
INTRODUCTION
Motivation & Background. Modeling progressive changes the brain vital for early diagno- sis of neurodegenerative diseases and effective treatment planning (Paulsen et al. (013).. However, the task is highly challenging due to the scarcity of samples. That is, the data are collected from longitudinal visits from individuals over a long period, and they become significantly limited and im- balanced due to increased mortality as the disease worsens. Moreover, it requires sophisticated neu- roimaging techniques such positron emission tomography (PET) and magnetic resonance imaging (MRI) to observe the progression in-vivo, which are expensive in cost, labor and time, and often in- volve exposure to high radiation level (Hosono al. 2021). aggravating the data scarcity problem.
Several neuroimaging initiatives such as ADNI (Mueller et al. 2005). OASIS (LaMontagne et al.) 2019) and WRAP (Johnson al., (0188) try to tackle this problem by collecting data from large cohort over a decade with several follow-up visits from individual subjects. They consist of a popula- tion of sequences of samples that provides information on longitudinal disease trajectories. Previous longitudinal studies have yielded successful results such as predicting the future evolution of individ- uals risk of AD (Marinescu et al., 2018) and imputing missing outcomes within trajectories (Luo) et al. 2016) by fully exploiting the dataset when sufficient sample size became available.
Alternatively, rather than waiting for individuals to be affected by neurodegeneration, one may uti- lize generative methods to obtain real-like synthetic longitudinal samples. Conditional generative models (Hwang et al. 2019 Yang et al. 202 have shown promising results in creating sequential data from scratch using time-varying diagnostic labels as conditions. However, these methods over- look the prior information of the condition which can be critical such as the irreversible nature of neurodegeneration. Moreover, these methods do not consider discontinuities in sample points caused by long intervals between clinical assessments (often ranging from 6 months to years) (Mueller et al. 2005), and this inconsistency is major practical issue in longitudinal disease analyses.

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Proposed method. To address the issues discussed above, we propose Conditional Diffusion model using Ordinal Regression (ConDOR), which generates long-term sequences conditioned on various ordinal factors. In this work, ConDOR is specifically applied model the progression of degen- erative disorders by synthesizing brain regional measurements based on disease-relevant metadata, such age and sequential diagnostic labels that descrihe disease progression. These factors, which change monotonically over time (c.g., increasing age and deteriorating labels), serve as conditions to characterize disease trajectories and generate realistic brain measurements from imaging scans.
Specifically, ConDOR operates as an autoregressive model, sequentially generating samples from baseline to follow-up time points with a diffusion model to address the temporal heterogeneity among subjects. To tackle data discontinuities caused by long intervals between collections, Con- DOR gradually generates unobserved interim samples, conditioned on interpolated ages and labels between consecutively observed time points. These pseudo-samples are crafted as combination of two components: cohort-level and subject-level samples. cohort-level sample is modeled with an ordinal regression (Winship & Mare 1984) fitted to the entire population to explicitly learn the globally common transition pattern in ordinal factors. On the other hand, individual variability is in- corporated subject-level sample obtained by interpolating samples in consecutive visits, which captures characteristics unique to individuals with aging and various disease manifestation patterns. Ultimately, these cohort and nubject-level samples are combined to form unobserved interim pseudo- samples, and CoRDOR iteratively estimates the difference in these consecutive pseudo-sample to reconstruct the subsequent observation the next time point. Such concept of separately modeling consistent group-level and variational sample-level features has been traditionally studied in ma- chine learning and computer vision, e.g., face recognition models that integrate common face with personal traits (Becerra-Ree Riera et al., 2019: Yan et al. 2022) and graph models that aggregate features from global semantic clusters and local node similarities et 2021: Kuang et al. 2019).
Furthermore, to address the limited sample-size issues in medical data, we introduce an extended framework of COnDOR that learns data from multiple datasets by using an additional domain con- dition. This approach maximizes the utility of available data from diverse sources, thus enhancing the model's s robustness and applicability. By flexibly utilizing both time-dependent (i.c., age and la- bel) and time-independent conditions (i.e., domain), ConDOR can be potentially applied not only to various medical data but also to other data types where data are scattered over various sites, making it versatile model for wide range of applications.
Contributions. Our contributions are summarized as follows. 1) We propose a novel generative model for longitudinal data, conditioned on ordinal factors such as age and disease severity. By in- corporating ordinal regression into a diffusion model, our method effectively captures the ordinality of conditions. 2) To handle temporal heterogeneity within visits, our method sequentially gener- ates samples that seamlessly fill gaps within sparse data points. These interim samples capture both population-level trends and individual-specific features by a dual-sampling approach, which leads to generating personalized longitudinal data. 3) To maximize the utility of limited data, the frame- work is extended enable the model to learn data from different sources with domain condition. By integrating both time-invariant and time-dependent factors, ConDOR improves generalizability across diverse datasets while capturing common progressive features.
As a result, ConDOR demonstrates its generality and efficacy on four independent AD biomark- ers, provided by Alzheimer's Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS). Also, ConDOR yields interpretable results at the brain regional level, validating that the generated results characterize realistic AD progression.
METHOD
In this section, we introduce "ConDOR", method for generating sample sequences with time- varying ordinal conditions. We first introduce the details of the task that we aim to solve and the way of sampling from conditional density function using Bayes' Theorem and ordinal regression, which forms the cornerstones of our model. Subsequently, we explain how the sampling strategy is integrated into a diffusion model, and further describe an extended version for learning data from multiple sources.
2.1 PROBLEM DEFINITION: DATA GENERATION WITH ORDINAL CONDITIONS
Consider a longitudinal sequence of samples (æ, )T where the samples for t = 1, 1,... T time points (T > 2) are presented in chronological order. Each sample a, E RB represents set of
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independent features time t, e.g., set of brain measurements obtained from B brain regions of interest (ROIs). For each time point, the samples come with ordinal conditions, e.g., age {ar and diagnostic labels {yr Y within disease spectrum, where 3/ E {l,..., C} denotes the disease progression from the healthy control state (y+- = 1) to the most deteriorated state (y:- C).
This study aims to characterize the progressive disease patterns and generate longitudinal sequences that comply with the ordinal conditions. Assuming that the brain regional measurements I3 as re- alizations of a random vector X [X1, [Xi,.., Xa) and age de and disease stage y/x are realizations of random variables A and Y respectively, a sample distribution is defined as 2t ~ [x]A,Y (2t, (Gt: yt). Here, the fx /xJAYY (zta (4, y/t) is a conditional probability density function (PDF) indicating the distri- bution of brain measurements for given age and disease stage. This formulation allows simulate realistic progression scenarios by considering both age and disease-specifeee variations in the brain.
2.2 REFINING CONDITIONAL PDF WITH BAYES' THEOREM
1763). the conditional PDF fx]Ar ( yo) is formulated as Using Bayes' Theorem Bayes
fx|A,y (xrla, v1) Py x,a æ az) f
( (s))
which enables the decomposition of the complex, high-dimensional distribution into interpretable components. The first term PY) (Belar, at) represents a probability mass function (PMF) that subject a disease stage Y/ for given brain measurements and age. Given that ys is discrete and ordinal variable, the PMF can be effectively modeled using ordinal regression (Winship & Mare 1984) to capture its ordinal nature. The second term fx|A ( |a,) is a prior distribution characteriz- ing age-relevant effects in estimating z;. As do not assume any shape such as ordinality for It, it needs to be directly estimated from given data using a non parametrii method such as kernel den- sity estimation (KDE) (Parzen 1962). Lastly, the denominator PY (Vela,) (a,) & Pr(Y = ya|A = ae) represents the probability of being at stage Ye given age at, which serves following sections, we introduce detailed methods of modeling P x (Yel zt, 0e) and fx (z) (ae) to estimate the conditional PDF f (2: 3/s) and describe the sampling process of a, from the estimated PDF using inverse transform sampling (Devroye 1986).
scaling constant. In the
Modeling ,Y (3ee Øe, ax) with ordinal regression. As Y denotes discrete ordinal categories that describe the natural degenerative progression of disease (i.e., healthy disease), the distribution Py æ 0e) - Pr(Y ye X Zz, A az) can be effectively estimated using ordinal re- gression model. Unlike nominal classifiers that treat all labels independently, the ordinal regression accounts for the ordered nature of ranked groups, ensuring that gradual transitions in disease stages are captured. This approach leads to more accurate predictions and meaningful interpretations, as the model explicitly considers that the difference between non-adjacent stages (e.g., healthy vs. dis- ease) is more significant than the difference between adjacent stages (e.g.. healthy vs. prodromal). Also, since brain measurements X are key biomarkers that reflect the disease progression (Counts) et al. (017)) and age A is risk factor of neurodegenerative diseases (Brown et al. 2005), using such factors as features of an ordinal regression enables effective estimation of the disease stage Y.
Given the ordered categories E (1,...,C) C}. the probability of being at or below a certain stage yr computed using cumulative probabilities as follows
Pr(Y < yt X 3t, A ax) = (b(TT) - -Bxar at),
(2)
where (6-) is the logistic function defined (xx) I+empl-a] and B's are regression coefficients.
The parameter Tye is a threshold that separates the y1-th stage from the next (y: + 1)-th stage, satisfying Ti < <... < TC-1- The above equation further allows us to derive the probability of being at the stage ye by taking the difference between consecutive cumulative probabilities as
Pr(Y = yt X = Zt, A = az) = 2 (T 3x. xTa)) ( 3xx; - -aTa)),
(3)
where = oc and TC = oc. To obtain the optimal thresholds, this ordinal regression model is fitted for N sequences with the following objective function
N
T C
L(O, 8x, BA) = NT ΣΣΣ
[()))" = c) log(Pr(Y = cl =(xx)" ",,",,A A= (at)")), (4)
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pseudo-sample
x 237
2)
H Eg ~ Et
ordinal regression
Forward process
Reverse process
Prixa (x)
x Txxar((x
Pyja (vcla))
cohort-level sample
x
X--1
EΦ
Ax
X
XT
Time
age: a1 label: y1
age: dr-1
age: of label: y
age: at label: yt
age: dy
label: yt-1
label: yr
Figure 1: Overview of ConDOR. ConDOR generates longitudinal sequence { conditioned on ordinal factors such age {ar Y and progressive labels (y:)² Baseline data 21 is generated by Regional Diffu- sion Model Eo(-) that estimates Gaussian noise ef ~ (O, 1). To capture temporal changes within a sequence, ar sampled every 1..., diffusion step between two data points adjacent in time {æt-1, 2=). The ax is combination of cohort-level and subject-level samples (i.c., # and æ(") that considers general trend the cohort-level and subject-specific progression for given conditions, respectively. Given the a;"" Temporal Diffusion Model (-) learns the difference Az," = x; x to generate follow-up data { {., }
where [(y = c) is an indicator function that outputs if the label yt is c and 0 otherwise. With this loss, thresholds are optimized to maximize the likelihood of accurately predicting ordinal samples.
Modeling fx a (xx (a.) via kernel density estimation. As the distribution of æt is unknown, we use -on-parametric KDE to estimate /' (2)+)rr) from the available data. Given ROI-wise mea- surements x; = [1,1 R2 E R, the prior distribution fxIA(<zll
(x)(a) is derived as
fx(a()))o)) II fx.1A(2(,(lo))
II
1 N
Σ
Dr.b (Ir,,))) k(
(5)
hb
hb
where ho is bandwidth of the Gaussian kernel k(-)- By integrating this distribution with the ( [t, ae) from equation 3 the (x)A,y(Zzlau. Vr) is derived as in equation
Inverse transform sampling of æ. After estimating the conditional PDF fx (2x (at, ye). inverse transform sampling (Devroye 1986) is performed generate the brain measurements 2; given its age and disease label. This is done by calculating its cumulative distribution function (CDF) as
B II 6m
tt.b fx, ( du,
Fx
Fx.jarr(uusoou Bi) = II bm 1
(6)
which denotes the probability that X, take values less than or equal to Ft,5 for given conditions or and ye. Thus, given = [u1,..., up] ~ Uniform(0, 1)ah the inverse CDF Fx A (u (u az Vc) finds the æ. [ -.. Ft. rx] such that each element satisfies Fx.lA,Y (Fr,,lae, yr) ub.
2.3 CONDOR: CONDITIONAL DIFFUSION MODEL USING ORDINAL REGRESSION
Fig. |illssrates the overall architecture of ConDOR that generates longitudinal samples J given a sequence of ages {or) - and labels {yr As the { is an entangled representation of both spatial and temporal features, our method characterizes each feature by using two separate diffusion models: Regional Diffusion Model (RDM) cạ(-) and Temporal Diffusion Model (TDM) (.).) parameterized by and ại respectively. Specifically, ConDOR operates as an autoregressive model, where RDM generates the sample for baseline time point æT, and TDM sequentially gen- erates subsequent samples {æx, )T= While RDM captures features from distinct regions within the data, TDM captures temporal features at both cohort-level and subject-level by combining two sep- arate samples: one is derived from a whole cohort distribution and the other is estimated from an individual sequence. The details of each diffusion model are given below.
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2.3.1 REGIONAL DIFFUSION MODEL FOR BASELINE DATA GENERATION
Since sample 21 at baseline time point is inherently absent of temporal prior features, RDM gen- erates the baseline data by only accounting for their spatial representations. Building upon the De- noising Diffusion Probabilistic Model (DDPM) (Ho et al. 2020). RDM is crafted as a conditional diffusion model that treats æt (L 1, .... T) as independent cross-sectional data. Its forward process dl q()) gradually adds Gaussian noise e ~ NN, 1) to a, for D diffusion steps as
1:D [.)) = II g(
a(a aa xt
II N( V B/a d- B(1). I), d=1
d=1
where æςA 2e and ( a variance schedule of the Gaussian distribution. During training, a reverse process (-) reconstructs samples conditioned on a, and ys by estimating the noise as follows:
0:D ac vn) == p(=?) Nat polaf ae yr. d), I(I), (o(
where the mean of Gaussian distribution 10 (1.44...000 ar Nr d)) is determined by a neural network ca(2; (e yr, d) (i.e,, conditional U-Net (Ronneberger et al. 2015)). To reconstruct samples from a complete Gaussian noise, RDM is trained to estimate the diffusion step-wise noise of with the following loss
LRDM =
N. ca(af de, Vr, d))?;
so that the baseline time point data are produced during the sampling process.
2.3.2 TEMPORAL DIFFUSION MODEL FOR FOLLOW-UP DATA GENERATION
To characterize temporal features within sequences, TDM is trained to learn changes among samples different time points. As prior samples are highly likely to affect subsequent data, TDM operates as an autoregressive model that sequentially reconstruets the follow-up sample from the previous one, using the prior as a reference. Specifically, while RDM generates 31 from Gaussian noise, TDM generates 2t (1 2 2) based on the prior data 1; In other words, TDM treats the previous data like a complete noise 2 in RDM, thereby eliminating the need for forward diffusion since the noise (i.e.. baseline data) is already given. The reconstruction of follow-up data is done by reverse diffusion for steps between every data pair adjacent in time {æx- 2 ) i.c., sampling pseudo- d= samples ) for each pair. Similar RDM which estimates stepwise noises, TDM estimates the difference between æ. - and a. enabling the model learn temporal changes efficiently.
Given that the diffusion steps d = 11 I,.., D of TDM correspond to the subdivided time between the real time points 1 and t, the diffusion step-wise age of and label yf are defined as follows:
d a = =0-1 (a+ -oe--a11)) and vf = min {c E (I....,C] c Ut-1 + (y-- - -h----11
d
} (10)
The af represents an interpolated age between ot-1 and dr, and the of indicates a discretized label for the intermediate diffusion step. For example, if yt-1 is 1 (e.g., healthy) and the following label Yt is C' (e.g., the most deteriorated stage), yf sequentially advances from I to C' as the diffusion progresses. These interpolated conditions allow TDM to account for smooth transitions between different time points and incorporate temporal dynamics into the diffusion process.
Integrating cohort-level sample & subject-level sample. Given conditions of and v the pseudo- sample of at diffusion step d is derived as a linear combination of o and oद as follows:
x Xa. + (1 -
(11)
where atd ~ y a4 v²) is cohort-level sample drawn from the overall cohort distribution defined in equation [ This represents a sample that captures general trends of a population based on the given age and label. In contrast, क = x;-1 + (xx xz-1) 1) D is a set of interpolated brain measurements between two consecutive time points. This accounts for individual-spee -seetfffi changes in the brain over time. The À E [o. 1] is a hyperparameter that balances the trade-off off between cohort and subject-level information. Higher À emphasizes the global pattern at the cohort level, while lower À focuses more on the subject-specing trajectory. This approach enables the model to integrate both population-wide wide and -ndivicual-ppecfffc features flexibly.
d is a subject-level sample, which
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Given the integrated sample z TDM estimates the differences Ax x -
x -x-
each diffusion
step 1,.,, D. where xf = 2/-1 and x, = zt. For 2,..., T, the model c approximates the difference Axf with the following loss function
LTDM
B ddd. [1 ca dt yr, d)]13]
(12)
so that follow-up samples {xt)(=) are reconstructed by learning detailed changes within sequences.
2.4 MULTI-DOMAIN LEARNING WITH DOMAIN CONDITION
Given that medical data analysis is inherently challenged by class imbalance and limited data avail- ability due to costly data acquisition processes, integrating multi-source data is necessary to ensure robust and generalizable learning. Therefore, ConDOR provides an extended generative scheme by integrating longitudinal data from multiple domains while preserving Somain-speciffe features. This is done by using an additional domain condition for reverse processes Regional and Tempo- ral Diffusion Models. Unlike time-varying age and label conditions, the domain does not depend on time, thereby an identical domain condition is consistently applied across all time points.
Regional Diffusion Model with domain condition. Given K domains, let my (k = L,.,, K) be a domain type. The reverse process of RDM with this additional domain condition defined as
D
O:D az m2) == p(a?) pe (a
Naa po(a oz, my d), 3(1)
(13)
d=1
where the μg is determined by neural network co(-) trained with the following denoising objective
LRDM = Be..d.cf
eg (xt ats Yt. mg, d)l??.
(14)
This allows RDM to estimate the noise el while incorporating the domain condition, so that RDM generates domain-specific data, enhancing the quality and relevance of the generated samples.
Temporal Diffusion Model with domain condition. Let N& be the number of sequences for domain ma, and M be random variable that denotes the domain condition. With the M, the equation is rewritten as a mixture distribution fx(A.Y,M()) as follows:
fxIA.YMM Mr, m+) = Σ as (x ye, m&),
(15)
where ay "E N₂ is mixing coefficient for domain-specifer PDF f (-). This mix-
N.
ture density allows small sample-sized domains (or domains with class imbalances) to be enriched by incorporating other larger domains (or domains with more balanced classes), thereby miti- gating the risk of overfitting to limited data. From the mixture density, a cohort-level sample a fx (A,Y, y. (x= laf yL mg) is obtained further construct the z as in equation 11 Along with the age and label conditions, the domain condition my is inputted into TDM c.(-) estimate the diffusion step-wise difference Azy x² x d- by using the following loss function
LTDM Ex, dt dw Axx e (xf at, Ut, Ma, d)l12
(16)
With this loss, the generated samples accurately reflect the underlying characteristics of each domain while still accounting for the ordinal nature the age and label conditions.
3 RELATED WORKS
Longitudinal Data Analysis. contrast to cross-sectional studies that focus on snapshot of data at single point in time, longitudinal data analyses focus on understanding temporal dynamics within data over time. This approach is widely used modeling time-series data in various do- mains such as healthcare (Mosquera et al.; 22033 Yoon al. 2023 Hwang al., 2019), traffic flow forecasting (Shu et al.] [021]LLi & Zhul 2021). and computer vision tasks such as human motion recognition in videos (Chen al. [202]] Cheng et al. 2020). In particular, studies in the healthcare domain include tracking electronic health records (Joshua Lin et al. 2022). predicting adolescent brain development (Holm al. 2023) and modeling the progression of diseases (Hwang et al.

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2019). By tracking health outcomes over time, these long-term studies contribute to the understand- ing of the progression of disorders and provide critical insights into how patient outcomes evolve.
Generative Models for Tabular Data. Tabular data are ubiquitous in various fields such as medicine, economics, and marketing, often involving a mix of discrete and continuous variables.
Recent generative methods handle both types simultaneously (Xu et al., 2019] Zhao et al. 2021 Kotelnikov et al., 2023), rather than focusing on either type (Choi et al.) 2017). While these meth- ods have shown successful results on tabular data, many limited to cross-sectional data, failing to capture temporal dynamics in longitudinal data. This shortfall is particularly critical in healthcare, where understanding the evolution of patient health is essential for precise prognosis and treatment planning. To address the challenge, our method focuses on generating realistic longitudinal tabu- lar data (i.e., biomarkers) that not only considers the intricate relationships between heterogeneous variables but also accurately characterizes temporal features across different time points.
EXPERIMENT
In this section, we describe the quantitative comparison of ConDOR with nine baseline methods and discuss the effect of model components along with interpretations. Overall, we performed experi- ments four different biomarkers from MRI and PET images provided by two independent lon- gitudinal Alzheimer's 's disease (AD) studies: Alzheimer's Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS), whose demographics and preprocessing meth- ods are reported in Appendix [A] Also, we provide detailed implementation settings of ConDOR in Appendix B and extensive qualitative comparisons with the baseline models in Appendix. D
4.1 DATASETS
ADNI, ADNI study (Mueller et al. 20055) is the largest long-term study of AD, aimed at collecting a an extended period. Four AD-associated biomarkers (Ortner et al. 2019) collected from MRI and PET scans were used: (1) Cortical Thick- ness (CT) from MRI, Standardized Uptake Value Ratio (SUVR) of (2) Amyloid, (3) fluorodeoxyglu- cose (FDG), and (4) Tau from PET. From N=2153 subjects, we excluded those with a single time point, resulting in 178, 687, 678, and 166 subjects for CT. Amyloid, FDG, and Tau respectively, with time points T per participant ranging from 2 to 10. All biomarkers were measured from 148 ROIs parcellated based on the Destrieux atlas (Destrieux et al. 2010). Five diagnostic labels were used: Cognitively Normal (CN), Significant Memory Concern (SMC), Early Mild Cognitive Impairment (EMCI), Late MCI (LMCI), and AD, with the disease progressing irreversibly from CN to AD.
comprehensive set of biomarker data from participants
OASIS. Compared to the ADNI, OASIS dataset (LaMontagne al., 2019) provides relatively small data where only Tau is available for N=32 subjects. All subjects have two time points, spaced 6 months apart, each labeled CN or AD. Among the 32 subjects, three were diagnosed with AD, where only one of them was consistently diagnosed with AD at both time points, while the other two transitioned from CN to AD. As in the ADNI, Tau was measured at 148 ROIs based on the Destrieux atlas. Due to the small sample size with a biased label distribution, single-domain learning on the OASIS dataset is highly prone overfitting Thus, performed multi-domain learning the Tau of ADNI and OASIS together with a domain condition to improve the model's generalizability.
4.2 EXPERIMENTAL SETUP
Baseline methods. We utilized nine baseline models, encompassing various types of generative models such as normalizing flow, generative adversarial networks (GANs), variational autoencoders (VAEs), diffusion models, and traditional interpolation-base synthetic techniques. Specifically, SMOTE (Chawla et al. 2002) is an interpolation-base convex combination of real data point with its k-thh nearest neighbor. This is a simple yet effective solution as demonstrated in (Camino et al., 2020, Kotclnikov et al.) 2023), where it outperforms GANs and diffusion models for tabular data generation. Also, we adopt Conditional Recurrent Flow (CRow) (Hwang et al.] 2019), a conditional normalizing flow model that generates long-term sequences. We also included GANs such as Conditional Tabular GAN (CTGAN) (Xu et al. 2019
method that synthesizes data points as a
Conditional Table GAN (CTAB-GAN) (Zhao et al.) 202I). and CTAB-GAN (Zhao et al. 2024
For VAES, we adopt Generative Modelling with Graph Learning (GOGGLE) [Lu et al. (2023) and
TVAE, which is VAE (Kingmal 2013) for tabular data generation introduced in (Xu et al. 2019).
Lastly, diffusion baausi models such as TabDDPM (Kotelnikov et al. 2023) and a conditional form of Denoising Diffusion Probabilistic Model (DDPM) (Ho al. 2020) adopted.
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Table Generation performance for single-domain learning on CT. Amyloid, and FDG test sets, with averages
and standard deviations from three replicates. The best results are in bold, and the second- best are underlined.
Cortical Thickness
Amyyoid RMSE
FDG
Model
WD
RMSE
JSD
WD
JSD
WD
RMSE
JSD
SMOTE
8.68 + 0.0
0.57 + 0.0
0.025 +.000
5.82 + 0.0
0.34 - 0.0
0.44 + 0.0
3.19 + 0.0
0 0.10 0.10++0.0
0,002 D.D
0.78
0.001
0.03
0061
0.001
2
0.007
0,012 1.0210000
CTGAN
0.12
0.37 +: 0.005
0.022
0.001
11.00 0.02
0.43 = 0.001
0.066
0.0
4,52 2 0.02
0.13 4: 0.001
0.003 4: 0.0
CTAB-GAN
6.43 + 0.29
0.35 + 0.033
0.016 0.001
+
0.42 0:04
0.23
+ 0.004
3.47 + 0.03
0.11 + 0.002
0.002 +.D
CTAB-GAN+
0.34 0.044
0.014
0.35 0.29
0015
0.002 1:00
GOGGLE
8.05 0.39
0.34 1: 0.016
0.020 0.001
16,02
0:16
0.65 0.006
0.010 0.0
9.33 0.22
0.25 0.006
0.010 1. 0.002
TVAE
5.99
0.38 + 0.063
0.013 + 0.003
1.24
+ 0.21
0.39 = 0.000
0.015 + 0.002
4,52 1:52=000 0.22
0.16 + 0.019
0.004 0.001
DDPM
9.94
0.59
0,028
0.017
2:51
0.026
0.30
0,001
0.001
TahDDPM
14.23 0.00
0.61
1: 0.0
0.070
0.001
31,28 1 0.05
1.18 0.001
0.145
1: 0.001
11.59 1: 0.04
0.32 0.001
0.018 0.0
CooDOR
4.25 = 0.02
0.21 # 0.002 0.007 0.001
5.27
#: 0.09
0.31
= 0.012 0.008 0.001
2.49 0.02
0.09 0.001
0,001 # 0.0
Table 2: Generation performance for multi- learning on Tau of ADNI and OASIS test sets. The average of three replicates and their standard deviations are reported along with the generation time for sampling 36 sequences (i.c., the number of test data) and the average time per sequence.
Model
WD
RMSE
JSD
Test set gen. time (s) Per-seq. gen. time (s)
SMOTE
7.166 0.0
0.460 + 0.0
0.029 - 0.0
29.35
0.83
CRow
9.494
0.188
0.599
0.027
0.045
0.045
1.39
0.04
CTGAN
19:545 +: 0.416
0.441
0.014
0,280
0.025
2.97
0.08
CTAB-GAN
8,950 0.5122
0.455 + 0.036
0,078
0.011
26.60
0,74
CTAB-GAN+
7.738 + 1.211
0.393 + 0.048
0.034
0.005
48.90
1.36
GOGGLE
8,380 0.4455
0.343 1
0.012 0.0
2.08
0.06
TVAE
5.096 0.303
0,300 0.020
0,018
0.000
4.33
0.12
DDPM
9.671 + 1.738
0.649 + 0.235
0,032
0.014
81.12
2.25
TabDDPM
50.592 1: 0.404
1.890 1 0.018
0.400 0.0
151.09
4,20
ConDOR (Ours)
5.625 0.040
0.293 0.011
0.012 0.0
65.7
1.83
Evaluation. Following prior work (Kotelnikov et al. 2023). three metrics were used to evaluate
the difference between generated samples and the test data: (1) Wasserstein distance (WD), (2) Root mean squared error (RMSE), and (3) Jensen-Shannen divergence (JSD). WD measures the expected minimum distance to transform one distribution into another, primarily reflecting differences in the global structure of the two distributions. In contrast, RMSE emphasizes detailed sample-wise differences, as it calculates the squared error for each pair of points. Similarly, JSD is sensitive to imbalances between distributions, capturing the differences in distributional shape and entropy. For all experiments, we used 80% of the whole data for training and the rest 20% for testing. The number of sampled data is equal to the number of test data in each respective experiment. All basclines and our model were trained three times to report their average results with standard deviation.
4.3 QUANTITATIVE RESULTS
Single-domain learning. Table I presents the quantitative results from the single-domain experi- ments on CT, Amyloid, and FDG. In all experiments and across all metrics, ConDOR consistently outperformed all baseline methods. Specifically, in the CT experiment, ConDOR demonstrated far smaller RMSE by a margin of 0.57 over CRow and at least 0.13 over GOGGLE and CTAB-GAN+ In the Amyloid experiment, ConDOR achieved up to 26.01 lower WD than TabDDPM and at least 0.1 lower than CRow. Although the margin over CRow is small on WD, our method significantly outperformed CRow on RMSE and JSD by margins of 0.54 and 0.053, respectively. Note that RMSE and JSD are sensitive sample-wise differences and distributional imbalances, while WD mainly focuses on global structural differences, such as mean differences between distributions. Thus, these results suggest that ConDOR more effective capturing individual characteristics with high variance compared to CRow. In the FDG experiment, ConDOR surpassed all basclines in WD and RMSE, and both our method and DDPM achieved the best result on JSD.
Multi-domain learning. As the sample size of the OASIS is small and label distribution is biased, the Tau of ADNI and OASIS were merged into unified dataset and learned together using domain condition. Table shows quantitative results from the unified dataset and sampling times. ConDOR surpassed eight out of nine baselines across all distance metrics and achieved comparable results to GOGGLE and TVAE. Specifically, our method and GOGGLE showed the same 0.012 on JSD, and TVAE surpassed our method on WD by ~0.55. However, ConDOR far outperformed GOGGLE on WD and RMSE by ~2.7 and 0.05, respectively, and exceeded TVAE on RMSE and JSD. These results suggest that although TVAE better estimates the overall distribution shape, our method excels in preserving finer details by capturing outliers and subtle differences at specific data points.
To assess computational efficiency, we measured the time taken to generate 36 sequences, corre- sponding to the test data size. As a result, CRow was the fastest taking 1144 seconds, and our
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Sumpled Ground Truth
(carly onset) (no progression
age: 79.1 / lahel: EMC1
age: 81.1 label: EMCI
age: N4.9 / label: AI)
Sampled Sampled
EMCI EMCI
front sup frout InF-Traagull
G_and 8 cingul-Ant
age: 84,9 / label: EMCI
age: 60 / label: EMCI
age: 61 / lnbel: EMCI
age: 62 / label: AD
1
2
t t=3
Time
Figure 2: Visualization of generation results from the FDG experiment (subject ID: 130.S 2403).)). The first
row shows the ground truth sequence with three time points and the second panel shows the generated sequenee from ConDOR for the same temporal conditions which highly resemble the real samples. In the third row, brain measurements are generated assuming the disease has not manifested at t = 3. while the bottom shows the sampled results with the same lahel condition as the ground truth with younger ages in sixties.
OASIS
ADNI
2.2
Ground Truth
t=1
t= 2
t=1
t= 2
Sampled
Sampled (domain shift)
ADNI
OASIS
0
Time
age: 70.0/label: CN
age: 70.5/label: AD
age: 70.8/label: EMCI
age: 71.8/label: AD
Figure 3: Visualization of generated results from the Tau experiment and results with switched domain con- ditions. The top panel is the ground truth of two samples with two time points (subject ID: OAS30818 and 129 S 4422 for OASIS and ADNI, respectively), where the data from different domains show different char- acteristics. The second panel shows generated results from ConDOR, and the bottom panel shows results with reversed domain conditions while age and label are consistent.
method took ~66 seconds. In general, this increased sampling time was typical for diffusion-based methods such as DDPM, TabDDPM, and ConDOR, due to the iterative denoising steps in the sam- pling process. However, as shown in both TableTand Table the sample quality of our method far surpasses other models, showing a trade-off between quality and computation speed.
4.4 MODEL BEHAVIOR AND ABLATION STUDY
Analyses on conditions. Figures 2 and illustrate qualitative results from ConDOR on the FDG and Tau experiments. respectively, highlighting the impact of label, age, and domain conditions. Given that FDG SUVR generally decreases with AD progression (Mosconi et al. 2009) while Tau SUVR increases (Sjögren et al., 2001). these trends are accurately reflected in the generated re- sults. For example, the top row Fig. 2 is the ground truth and the second row is the generated sequence from ConDOR with the same conditions, where regional results resemble the ground truth for all time points. The third row illustrates a label-consistent scenario, where the disease has not progressed from EMCI to AD. In this case, the FDG SUVR at t 3 remains higher than that of AD in the second panel, which demonstrates the sensitivity of ConDOR that captures subtle differ- ences between labels. One of the most prominent differences is shown in the superior frontal gyrus, where significant glucose reduction has been observed along the AD progression in various AD studies -Sanabria-Diaz al. 2013 He et al. 2015). While both the ground truth and generated
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Table 3: Ablation studies on the cohort-level sample weight for all experiments.
ADNI
ADNI=OASIS
A
Cortical Thickness
Amyloid
FDG
Tau
WD
RMSE
WD
RMSE
WD
RMSE
WD
RMSE
4.423
0.115
0.208 +: 0.003
5.608 +: 0.070
0.321 +: 0.010
2.551 4: 0.072
0.086 + 0.002
6.628 4: 0.286
0.334 + 0.016
0.1
4,252
= 0.024
0,205 +: 0.002
5,400 +: 0.139
0.313 + 0.012
2.487 + 0.015
0.085 + 0.001
6.172 +: 0.188
0.320 + 0.007
0.3
4.368
0.135
0.208 0.007
5.522 0.173
0.296 0.012
2.512 0.002
0.086 0.002
5.833 0.1663
0.313
0.5
4.372 = 0.064
0.207 + 0.0004
5.541 + 0.088
0.326 + 0.088
2.595 + 0.031
0.088 + 0.001
5.692 + 0.066
0.305 + 0.008
0.7
4,496 = 0.035
0,215 + 0.002
5,530 = 0.086
0 + 0.012
2.567 + 0.024
0.087 + 0.001
5.645 + 0.014
0.292 = 0.010
0.9
4.372
0.083
0.217
+ 0.012
5.629 + 0.029
0.309 0.007
2.632 + 0.108
0.088
+ 0.002
5.999
+ 0.223
0.313 + 0.003
4.432 = 0.122
0.209 + 0.005
5.852 + 0.287
0.331 + 0.008
2.620 + 0.046 0.088 + 0.002
5.832 + 0.207
0,313 + 0.023
results with the AD label show relatively low FDG SUVR in this area, the sampled EMCI results at the same age display higher values, resembling the ground truth of the EMCI.
On the other hand, in the early-onset AD (EOAD) scenario (i.e., AD diagnosed before the age of 65) on the bottom row, ROIS such as the cingulate gyrus and sulcus show higher FDG SUVR than the ground truth, which is known to be highly negatively correlated region with age (Jang et al., 2018). Also, it is worth noting that the triangular part of the inferior frontal gyrus of the EOAD shows lower values than late-onset AD (LOAD). This result aligns with established AD studies (Kim) et al. 2005 Kalpouzos et al. 2005). which have shown that EOAD features more focal reductions in glucose metabolism in the frontal cortex, while LOAD tends to have more diffuse hypometabolism.
Fig. 3 illlstratts results from the Tau experiment involving two samples each from the OASIS and ADNI datasets. Both samples span two time points with similar ages, yet the OASIS sample shifts from CN to AD, while the ADNI sample progresses from EMCI to AD. In the top row, the ground truth for AD of OASIS (2nd column) and AD of ADNI (4th column) show significant differences, despite similar ages, possibly due to differences in the data collection environment.
As shown in the second row, our method successfully captured these domain-speciie differences. Moreover, when domain conditions are reversed (3rd row), ConDOR not only characterizes the dis- tinct features of each domain but also accurately captures the positive correlation between Tau SUVR and disease progression. Specifically, the bottom left sample with the ADNI and CN conditions dis- plays lower Tau SUVR than the ground truth of the ADNI EMCI (top, 3rd column). Similarly, the EMCI sample of OASIS (bottom, 3rd column) shows intermediate values between the CN and AD of OASIS. Given that the original OASIS dataset has only CN and AD labels, multi-domain learning with other sources, such as ADNL-which includes intermediate MCI labels-allows broader spectrum of data. Such an approach empowers the model to learn the comprehensive, full progression from CN to AD, thereby enhancing its generalizability across different disease stages.
to generate
Effect of the cohort-level weight X. Table Tablee]presentt the result of the ablation study on the X, which balances the effect of cohort-level and subject-level samples used in TDM. For all experiments, us- ing both samples (i.e., 0 < À < 1) outperformed the settings using only subject-level (i.e., X = 0) or cohort-level samples (i.e., À 1) alone. In the single-domain experiments on CT. Amyloid, and FDG, A = 0.1 yielded the best results. On the other hand, in the multi-domain experiment with Tau, higher X's such as À= 0.7 and 0.5 produced the best and second-bes -bst results, respectively. These findings suggest that using both cohort-level and -ndividual-specifie features improves the sample quality regardless of the domain settings. However, subject-specific details play a relatively criti- cal role in single-domain learning. while capturing broader population-wict wide trends across multiple domains is more important when learning from diverse sources for effective generalization. Thus, by adjusting the X, the model can generate higher-quality samples across both homogeneous and heterogeneous data, with the choice of X varying based on the task and data distribution.
CONCLUSION
In this paper, we introduced ConDOR, a novel conditional diffusion model for generating longitudi- nal samples conditioned on multiple ordinal factors. When applied to the generation of costly lon- gitudinal neurodegenerative disease data, ConDOR addresses the data scarcity issue in medical data analyses. By incorporating an ordinal regression model into the diffusion process, ConDOR effec- tively characterizes the realistic ordinal dynamics of the disease. Also, the model generates smooth temporal samples by employing a dual-sampling strategy, which blends both individual-specht global characteristics obtained from the entire sample distribution. As a result. ConDOR outper- formed nine recent generative methods, underscoring its potential to enhance our understanding of the complex relationships between heterogeneous disease-related factors and disease progression.
and
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Reproduciblity Statement. To ensure the reproducibility of work, we provide detailed dataset description in Appendix A and implementation settings including all hyperparameters in Appendix B Regarding quantitative evaluations, all experiments were replicated three times and their mean with standard deviation reported. Pretrained ConDOR models for all datasets, and codes of ConDOR and baseline methods are availble at htttps://githtb: cttp Haomm/Hnna ConDOR- ICLR25
Acknowledgments. This research was supported by NRT-2022RI A2C2092336 (70%), RS-2022- I12202290 (20%), and RS-2019-1199106 (AI Graduate Program at POSTECH, 10%).
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In the appendix and supplementary material, present 1) the demographies of four biomarkers provided by ADNI and OASIS studies, 2) detailed implementation settings of ConDOR used for each experiment, 3) limitations of ConDOR and suggestions for future work, 4) extensive qualita- tive comparisons with baseline methods, and 5) a video illustrating a sampled sequence that shows changes in Amyloid SUVR over 20 years, which were not included in the main manuscript due to the page limit.
A DATASET DEMOGRAPHICS
ADNI (Mueller et al., 2005 is the largest open-source AD study, providing longitudinal and mul-
tisite neuroimaging data collected from 21 study sites. We utilized four AD-associated biomarkers
from the ADNI dataset: (1) cortical thickness (CT) from MRI, (2) SUVR of Amyloid from PET, (3) SUVR of floorodexyyguucose (FDG) from PET. and (4) SUVR of Tau from PET. total of 2153 subjects provided at least one MRI/PET image, with 1 1101 providing MRI for CT, 1205 providing Amyloid-PFT, 1447 providing FDG-PET, and 549 providing Tau-PET. From the brain scans, we performed preprocessing to obtain brain regional measurements. We used the Destrieux atlas (De- strieux et al. 2010) to parcellate the cortical surface into 148 regions using TI Tw-wiighted MR images by skull stripping. tissue segmentation, and image registration. Based on the tissue segmentation result, we measured the average cortical thickness in each region by Freesurfer. For the Amyloid, FDG, and Tau, calculated the region- wise average concentration level from PET scans. The cerebellum was used as the reference region to calculate the SUVR for each pathology modality.
Subsequently, removed subjects whose age label is missing and those who have only one time point. Consequently, we obtained 178, 687, 678, and 166 subject data for CT, Amyloid, FDG, and Tau respectively. The demographic details for these biomarkers are summarized in Table The number of time points varies across subjects, with a minimum number of two for all biomarkers. The maximum number of time points five for Amyloid, Tau, and CT, and ten for FDG. The average time interval between data collection points and their standard deviations are as follows: 2.2 + 0.78 years for CT, 2.2 + 0.72 years for Amyloid, 1.3 + 1.20 years for FDG, and 1.2 + 0.37 years for Tau.
The OASIS dataset (LaMonngee al. 2019) provided Tau-PET scans from 81 subjects. To caleu- late regional Tau SUVR, we registered the PET scans to Te-whighted images and computed standard uptake values (SUV) for each region based on the Destrieux atlas. Similar to the ADNI preprocess- ing, used the cerebellum cluding subjects whose age or label missing and those with only a single time point, we retained 32 subjects. All subjects have time points with 6-month interval between data collection. Of the 32 subjects, three were diagnosed with AD; one had consistent AD diagnosis at both time points, while the other two transitioned from CN AD. The demographic information for the OA- SIS dataset is presented in Table 5
the reference region to compute the SUV ratio (SUVR). After ex-
B DETAILED IMPLEMENTATION SETTING
To train ConDOR, we used PyToorch with a single NVIDIA GeForce RTX 3090 GPU. For all biomarkers, we applied stratified train-test split to the data, maintaining the ratio of the given five labels, with 80% of data used for training and the remaining 20% for testing. Also, for the multi- domain learning on Tau, we first combined the Tau datasets from ADNI and OASIS, and then applied stratified train-test split to the unified dataset maintaining the sample size ratio of each domain. To prevent biased results, all experiments were replicated three times with different parameter initializa- tion, and their average performance along with standard deviation were reported. In Table we pro- vide details of the implementation settings of ConDOR for all experiments on four biomarkers. We performed grid search to choose the best learning rate in {0.002, 0.0015, 0.001, 0.0008, 0.0005). and a batch size in {16, 32). In the reverse process of RDM and TDM, U-Net (Ronneberger et al, 2015) is used to implement (-)-) and c.).).
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Table 4: Demographics of the ADNI dataset. The numbers of subjects for each category were calculated based on the baseline time point samples. The number of records denotes the total number of cross-sectional samples across the population.
Biomarker
Category
CN
SMC
EMCI
LMCI
AD
# of subjects
50
32
64
23
Cortical Thickness
# of records
112
72
152
56
39
Gender (M/F)
26/24
24/8
40/24
13/10
5/4
Age (Mean + Std)
71.3 +
4.2
72.1
4.7
72.6 +
6.9
74.2 = 5.2
76.5
7.1
# of subjects
150
87
238
158
records
405
231
715
376
270
Amyloid Gender (M F)
79/71
56/31
138/100
88/70
31/23
Age (Mean + Std)
71.9 + 3.9
73.0
4.9
73.3 + 7.1
74.1 + 7.9
76.0 + 7.5
# of subjects
147
151
262
114
of records
415
345
966
580
FDG
Gender (M/F)
82/65
3/1
94/57
167/95
67/47
Age (Mean +: Std)
72.2 + 3.5
73.9
+ 4.0
75.4 + 5.8
76.6 + 6.9
77.2 d: 6.5
# of subjects
30
37
48
31
20
# of records
65
85
118
76
55
Tau
Gender (M F)
28/37
25/60
66/52
44/32
26/29
Age (Mean + Std)
68.4 + 3.7 68.9 3.8
69.8 + 5.9 71.0 + 7.4 78.8 8.4
Table 5: Demographics of the OASIS dataset. The numbers of subjects for each category were calculated based on the baseline time point samples. The number of records denotes the total number of cross- sectionatlionl samples across the population.
Biomarker
Category
CN
AD
of subjects
31
1
# of records
60
4
Tau
Gender (M/F) F)
13/18
1/0
Age (Mean Std)
63.2 = 7.5
71.9 + 1.6
Table 6: Hyperparameters of ConDOR for all experiments.
Hyperparameter
CT
Amyloid
FDG
Tau
Optimizer
Adam
Adam
Adam
Adam
Leaming rate
0.001
0.001
0.0008
0.0008
Train
Leaming scheduler
Multiplicative..R
Multiplicative..R
Multplicativel..R
Multiplicativel.k
Leaming rate decay
0.999
0.999
0.999
0.999
Batch size
16
16
16
16
Number of epochs
10000
10000
10000
10000
KDE
bandwidth Ng
0.001
0.001
0.001
0.001
Hidden dimension
64
64
64
64
Number layers
4
4
4
4
Number of initial channel
1
1
1
1
68
Number hidden channels
[64, 128, 256, 512]
[64, 128, 256, 512]
[64, 128, 256, 512]
[64, 128, 256, 512]
Number of final channels
Number of sampling steps
1000
1000
1000
1000
Hidden dimension
64
64
64
64
Number of layers
4
4
4
4
Number initial channel
Number of hidden channels
[64, 128, 256. 512]
[64, 128. 256. 512]
[64, 128. 256, 512]
[64. 128. 256, 512]
Number channels
Number of sampling steps
100
100
100
100
cohort-level weight
0.1
0.7
15

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Published as a conference paper at ICLR 2025
C LIMITATION AND FUTURE WORK
Limitations. (1) Compared to one-shot generative methods such as TVAE and GANs, our autore- gressive approach has longer generation time since samples are generated sequentially. The gap in the sampling time becomes significantly larger as the sequence length (i.e., the number of time points) becomes extended. (2) Also, our method may face challenges in scenarios where labels are abruptly reversed over time. In such cases, the interpolated label y/ may not represent feasi- ble disease severity and could deviate from the range of given observed labels, which may highly likely aggravate the training stability and model performance. In our experiments, we confirmed that all sequence labels are monotonically deteriorating, so the yf in equation 10 defined under (3) The four AD biomarkers used in the experiments (i.e., cortical thickness, SUVR of Amyloid, FDG, and Tau) are widely recognized and clinically validated biomarkers for identifying AD (Querbes al. 2009 Jack & Holtzman| (013). However, these biomarkers may not fully represent the broader spectrum of neurodegenerative diseases, such Parkinson's Huntington's 's disease, which involve different biological mechanisms. (4) Addi- tionally, the AD datasets utilized in our experiments primarily consist of participants from the US, potentially limiting the model's 's applicability to populations with different genetic, environmental, or lifestyle factors. This lack of population diversity could affect the generalizability of the findings across broader demographics.
the strict assumption of ordinal transitions.
Future Works. (1) While the dual-sampling approach in our method effectively balances both co- hort and subject-level information, may introduce biased results if the trade-off hyperparameter is not appropriately tuned. The ablation studies on the À in Table inddcatee that the bias is not critical general. However, considering the inefficiency of fine-tuning for every dataset, we plan to develop adaptive mechanisms that dynamically adjust the À based on dataset characteristics, ensuring opti- mal balance between cohort and subject-level contributions. (2) Morcover, we plan to extend our model by incorporating additional AD-relevant conditions, such blood plasma (Schneider et al. 2009 [Hansson et al. 2023). Along with the age and diagnostic labels, this biomarker could uti- lized time-dependent conditions and could provide complementary information to understand AD progression, ultimately enhancing the biological plausibility and robustness of the generated data.
16

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Published as a conference paper at ICLR 2025
D QUALITATIVE COMPARISON WITH BASELINE MODELS
1.0
4.8 (mm)
(a) Ground Truth
(b) ConDOR (Ours)
(c) SMOTE
(d) CRow
(c) CTGAN
(f) CTAB-GAN
(g) CTAB-GAN+
(h) GOGGLE
(i) TVAE
(i) DDPM
(k) TabDDPM
Figure 4: Example of ground truth and generated results from the CT experiment. This subject (ID: 029 S_4385) has two time points with age/label 68.2/CN at the first time point and 71.8/AD at the second time point. Each set, consisting of the outer right, outer left, inner left, and inner right hemispheres, shows the results from time point, with time points increasing from left right.
17

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Published as a conference paper at ICLR 2025
0.4
4.8
(a) Ground Truth
(b) ConDOR (Ours)
(c) SMOTE
(d) CRow
(e) CTGAN
(f) CTAB-GAN
(g) CTAB-GAN+
(h) GOGGLE
(i) TVAE
(i) DDPM
(k) TabDDPM
Figure 5: Example of ground truth and generated results from the Amyloid experiment. This subject (ID: 127_S_2213 has three time points with age/label 82.3/EMCI at the first time point, 84.3/EMCI the second time point, and 86.3/EMCI at the third time point. Each set, consisting of the outer right, outer left, inner left, and inner right hemispheres, shows the results from one time point, with time points increasing from left to right.
18

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Published as a conference paper at ICLR 2025
3e-3
2.0
(a) Ground Truth
(b) ConDOR (Ours)
(c) SMOTE
(d) CRow
(e) CTGAN
(f) CTAB-GAN
(g) CTAB-GAN+
(h) GOGGLE
(i) TVAE
(i) DDPM
(k) TabDDPM
Figure 6: Example of ground truth and generated results from the FDG experiment. This subject (ID: 037-S_1078) has three time points with age/label 70.6/LMCI at the first time point. 72.3/LMCI the second time point, and 75.6/AD at the third time point. Each set, consisting of the outer right, outer left, inner left, and inner right hemispheres, shows the results from one time point, with time points increasing from left right.
19

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Published as a conference paper at ICLR 2025
5e-3
9.2
(a) Ground Truth
(b) ConDOR (Ours)
(c) SMOTE
(d) CRow
(e) CTGAN
(f) CTAB-GAN
(g) CTAB-GAN+
(h) GOGGLE
(i) TVAE
(i) DDPM
(k) TabDDPM
Figure 7: Example of ground truth and generated results from the ADNI dataset on Tau experiment. This subject (ID: 023_S_1 119)) has three time points with age/label 76.5/EMCI at the first time point, 78.0/AD the second time point, and 79.3/AD the third time point. Each set, consisting of the outer right, outer left, inner left, and inner right hemispheres, shows the results from one time point, with time points increasing from left right.
20

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Published as a conference paper at ICLR 2025
5e-3
9.2
(a) Ground Truth
(b) ConDOR (Ours)
(c) SMOTE
(d) CRow
(e) CTGAN
(f) CTAB-GAN
(g) CTAB-GAN+
(h) GOGGLE
(i) TVAE
(k) DDPM
(k) TabDDPM
Figure 8: Example of ground truth and generated results from the OASIS dataset on the Tau exper- iment. This subject (ID: OAS30815 18) has two time points with age/label 70.0/CN at the first time point and 70.5/AD the second time point. Each set, consisting of the outer right, outer left, inner left, and inner right hemispheres, shows the results from one time point, with time points increasing from left to right.
21

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Published as a conference paper at ICLR 2025
E ADDITIONAL QUALITATIVE RESULTS: A VIDEO SHOWING 20-YEAR CHANGES IN AMYLOID SUVR
In the supplementary material, provide video showcasing qualitative results from ConDOR on Amyloid SUVR, illustrating the sequential changes of a subject aged 65 to 85, with five diagnostic labels transitioning from CN AD. Considering the baseline age distributions of the five labels used in the Amyloid experiment (Table D) the age range from 65 to 85 appropriately aligns with the real-world longitudinal samples labeled from CN AD. The video illustrates that the Amy- loid SUVR of the generated sample generally increases as the disease worsens. These results are consistent with the established patterns of Amyloid accumulation observed Alzheimer's disease, demonstrating the effectiveness of ConDOR in capturing the dynamics of the biomarker along the disease progression.
22


Reviews:
[{"review_id": "1Pv8xmVgMM", "reviewer": "Reviewer_rUXZ", "summary": "This paper introduces a novel conditional generative model for synthesizing longitudinal sequences to study neurodegenerative diseases such as Alzheimer’s disease. The method uses ordinal regression and a diffusion model to generate realistic disease progression imaging data.", "questions": "1. How does the proposed method theoretically ensure the accurate representation of disease progression, especially considering the complex dynamics and irregular intervals in longitudinal data?\n2. How does the proposed method theoretically improve upon existing generative models for longitudinal data? Are there any theoretical limitations or assumptions that need further clarification?\n3. The paper introduces a dual-sampling approach combining cohort-level and subject-level samples. How does this method compare to other state-of-the-art techniques in terms of capturing individual-specific features and general trends? Are there any potential biases introduced by this approach?\n4. The experiments are conducted on four AD biomarkers from MRI and PET images. How representative are these biomarkers and datasets of the broader neurodegenerative disease population? Are there any limitations in the experimental design that could affect the generalizability of the results?\n5. The paper claims superiority over nine baseline approaches. How robust are these results across different metrics and datasets? Are there any specific scenarios or conditions under which the proposed method might underperform or fail?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. Combing the cohort-level trend and subject-level trend for longitudinal data generation. \n2. Extensive validation on four Alzheimer's Disease biomarkers demonstrates the model's superiority over nine baseline approaches.", "weaknesses": "1. The paper lacks a comprehensive theoretical justification for the proposed method. While the method is innovative, a deeper theoretical comparison with existing models could strengthen the argument for its necessity and effectiveness.\n2. The description of the methodology, particularly the integration of cohort-level and subject-level samples, is somewhat convoluted. The paper could benefit from clearer explanations and more detailed algorithmic steps to enhance reproducibility.\n3. The paper does not provide a thorough statistical analysis to support these claims. The lack of confidence intervals or significance testing weakens the robustness of the reported findings.\n4. The discussion section is relatively weak in terms of interpreting the results and their implications. The paper does not adequately address the potential limitations of the proposed method or suggest directions for future research, which are crucial for a comprehensive understanding of the study’s impact.", "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": "4wuXiQ5rZ7", "reviewer": "Reviewer_xa3Q", "summary": "This paper proposes a conditional generative model for synthesizing longitudinal sequences. \nIt first uses ordinal regression and kernel density estimation to model the conditional PDF and then interpolate gaps between consecutive observations. \nTwo diffusion models are then trained to model baseline data and changes in follow-up samples. \nThese diffusion models generate disease progression data by sequentially sampling.", "questions": "RDM is designed to geneate the baseline sample $x_1$. However, during training, the authors use all the samples $x_t$ (t = 1, .., t) as independent cross-sectional data.\nThe justification for using such setting is not presented in the paper. \nFor example, why not use only $x_1$ to train the RDM? \nWill this setting cause the RDM to be biased as some longitudinal samples have longer records or are recorded more frequently\n\nAcoording to Table 3, the choice of hyperparameter $\\lambda$ significantly impacts the performance of the proposed method. \nHowerver, how to select $\\lambda$ is unclear, for example, which dataset and what metric do the author use to choose $\\lambda$.\nThe author used 80% of the whole data for training and the rest 20% for testing for all experiments,\nand it seems there is no validation dataset to optimize $\\lambda$.\nTherefore, the results shown in Table 3 is less convincing to me since they are propbably derived from either training or test set, \nand the results in Table 1 and 2 are also less convincing since we may not able to get the best $\\lambda$ in practice.\n\n\nThe training strategies for the generative model are somewhat unclear to me. For example do the authors train RDM and TDM seperatedly or jointly?\n$D$ seems to be another important hyperparameter, but how the authors chose $D$ is also unclear.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "The design of the proposed model's structure design is innovative, partsuch as the combination of two diffusion models and the use of both cohort and subject-level interpolation for training. \n\nThis paper provides clear comparisons to baseline models across multiple metrics and good visualizations.", "weaknesses": "Some abnormal results are not well discussed or explained. \nFor example, in Table 1, the variance in DDPM's performance is very high compared to other methods. \nSince DDPM is one of only two diffusion-based comparison methods, it would be helpful to provide an explanation for this abnormal performance.\n\n\nThe authors do not mention how to deploy the model. For example, how to use the trained model to generate new data. \nIf my understanding of the generative process is correct, we only need to use these two diffusion models with random noise as the input when generating new data.\nThere is no option to allow the two diffusion models to generate samples conditioned on specific ages and disease severity, \ne.g., we can't use age as an input for these diffusion models when generating, \nalthough the authors claim that this model can generate data conditioned on these factors.\n\nSome important technical details are also missing. Please refer to the questions below", "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": "VWewotCps5", "reviewer": "Reviewer_jkdK", "summary": "The paper presents ConDOR, a novel conditional diffusion model for generating longitudinal neurodegeneration data with ordinal disease progression factors. The model's architecture integrates both cohort-level and subject-level characteristics through a dual-component approach. At the cohort level, it employs Bayes' Theorem combining an ordinal regression model (capturing disease stage relationships) with a kernel-based conditional distribution. For data generation, ConDOR utilizes two diffusion models: a Regional Diffusion Model (RDM) for generating baseline measurements across brain regions, and a Temporal Diffusion Model (TDM) for generating subsequent longitudinal data. The model also incorporates a domain conditioning mechanism to integrate data from multiple sources. The authors evaluate ConDOR on multiple biomarkers (Amyloid, Cortical Thickness, and Fluorodeoxyglucose) from two prominent neurodegenerative disease datasets (ADNI and OASIS), comparing against nine baseline methods including GANs, VAEs, and other diffusion-based approaches.", "questions": "1. The model evaluation lacks clarity regarding whether the authors performed a subject-level or observation-level split. Specifically, did they keep all observations from each subject together, or did they split individual observations, potentially including different time points from the same subject in both training and test sets? It would be valuable to see how well the model predicts follow-up scans based on data from earlier time points, given that the Temporal Diffusion Model is a novel component. Additionally, for baseline models like DDPM that lack a temporal component, it would be interesting to understand how the authors utilize these models to generate follow-up scans over time.\n2. The Temporal Diffusion Model uses linear interpolation to model progression in age and labels, which may not be ideal, as transitions between disease states are often abrupt or follow complex patterns. Furthermore, it would be beneficial to see theoretical proof that such linear interpolation preserves the properties of diffusion models.\n3. Including some directions for future work in the conclusion would be beneficial for the research community.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The proposed model captures both spatial and temporal features through a combination of a Regional Diffusion Model and a Temporal Diffusion Model.\n2. This new generative model addresses challenges associated with sparse, irregular, and widely spaced intervals in medical data.\n3. The model strikes a balance between cohort-level and individual-level fitting, capturing generalized population trends while accommodating individual variability.\n4. It introduces a novel integration of ordinal regression with diffusion models.\n5. The experiments are comprehensive, with comparisons to nine baseline models, including GANs, VAEs, and other diffusion-based models, evaluated across three metrics. Implementation time is also compared.\n6. The model is extended to a multi-domain setting, enhancing its generalizability and applicability to different data sources.", "weaknesses": "1. The ordinal regression model might oversimplify the disease progression process. Additionally, the temporal diffusion relies on linear interpolation for temporal transitions, which may not accurately capture realistic disease dynamics.\n2. There is a lack of comparison with traditional longitudinal baseline models commonly used in medical literature.\n3. The model evaluation has not been clearly described. Did the authors split subjects into training and test sets, keeping all observations from each subject together, or did they split individual observations, potentially placing different time points from the same subject in both training and test sets?\n4. The reproducibility of this work is not guaranteed, as the code has not yet been made available.", "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 (Spotlight)