Learning Patient-Specific Disease Dynamics With Latent Flow Matching For Longitudinal Imaging Generation
Authors: Hao Chen
Rui Yin
Yifan Chen
Qi Chen
Chao Li
Venue: ICLR 2026 Poster (2026)
Keywords: Medical Image Generation
Longitudinal Analysis
Flow Matching
Primary area: generative models
TL;DR: ∆-LFM models disease progression as a velocity field with flow matching, aligning patient trajectories to be continuous, monotonic, and clinically meaningful for interpretable analysis across MRI benchmarks.

Abstract: Understanding disease progression is a central clinical challenge with direct implications for early diagnosis and personalized treatment. While recent generative approaches have attempted to model progression, key mismatches remain: disease dynamics are inherently continuous and monotonic, yet latent representations are often scattered, lacking semantic structure, and diffusion-based models disrupt continuity through the random denoising process.
In this work, we propose treating disease dynamics as a velocity field and leveraging Flow Matching (FM) to align the temporal evolution of patient data. Unlike prior methods, our approach captures the intrinsic dynamics of disease, making progression more interpretable.
However, a key challenge remains: in latent space, Autoencoders (AEs) do not guarantee alignment across patients or correlation with clinical severity (e.g., age and disease conditions). To address this, we propose learning patient-specific latent alignment, which enforces patient trajectories to lie along a specific axis, with magnitudes increasing monotonically with disease severity. This leads to a consistent and semantically meaningful latent space.
Together, we present ∆-LFM, a framework for modeling patient-specific latent progression with flow matching. Across three longitudinal MRI benchmarks, ∆-LFM demonstrates strong empirical performance and, more importantly, establishes a new framework for interpreting and visualizing disease dynamics.

Published as a conference paper at ICLR 2026
LEARNING PATIENT-SPECIRIC DISEASE DYNAMICS WITH LATENT FLOW MATCHING FOR LONGITUDINAL IMAGING GENERATION
Hao Chen + Rui Yin
Yifan Chen'
Qi Chen Chao Li Nanjing First Hospital, Nanjing Medical University
University of Cambridge, 3 Johns Hopkins University
University of Dundee
ABSTRACT
Understanding disease progression is a central clinical challenge with direct im- plications for early diagnosis and personalized treatment. While recent generative approaches have attempted to model progression, key mismatches remain: disease dynamics are inherently continuous and monotonic, yet latent representations are often scattered, lacking semantic structure, and diffusion-based models disrupt continuity with a random denoising process. this work, we propose to treat the disease dynamics as velocity field and leverage Flow Matching (FM) to align the temporal evolution of patient data. Unlike prior methods, captures the in- trinsic dynamics of disease, making the progression more interpretable. However, key challenge remains: in latent space, autoencoders (AEs) do not guarantee alignment across patients or correlation with clinical-severity indicators (e.g., age and disease conditions). To address this, we propose to learn patient-speciffc la- tent alignment, which enforces patient trajectories to lie along specific axis, with magnitude increasing monotonically with disease severity. This leads to a con- sistent and semantically meaningful latent space. Together, present A-LFM, a framework for modeling patient-specific latent progression with flow matching. Across three longitudinal MRI benchmarks, A-LFM demonstrates strong empir- ical performance and, more importantly, offers new framework for interpreting and visualizing disease dynamics.
INTRODUCTION
Modeling disease progression is fundamental problem in healthcare (Suk & Shen, 2013; Wang al., 2020), with profound implications for early detection and individualized treatment. Disease does not evolve uniformly: differences in anatomy, genetics, and environment give rise to heteroge- neous trajectories, which are an intrinsic property of disease dynamics (Real & Biek, 2007; Parratt et al., 2016; Li et al., 2025). Accounting for this heterogeneity is essential for accurately charac- terizing temporal changes, identifying preclinical biomarkers, and designing personalized therapies that can improve clinical outcomes (Frisoni et al., 2010). However, most progression models capture only population-leve trends, overlooking individualized variation (Rokuss et al., 2025; Yang et al., 2025b). This limitation obscures early-stage signals and misaligns disease severity with underly- ing anatomy, ultimately reducing clinical utility. Capturing patient-specific dynamics is therefore critical, but remains underexplored challenge (Lai al., 2025).
Recent advances in generative modeling have opened new opportunities for studying disease pro- gression. Traditional biomarker-based approaches often reduce complexity to coarse measures (e.g., volume changes (Jack Jr et al., 2003; Tabrizi et al., 2011) or disease rating (O'Bryant et al., 2008; Young et al., 2020)), which can obscure heterogeneous discase dynamics. contrast, longi- tudinal medical image generation offers a principled framework for visualizing symptomatic tran- sitions and individualized patterns of anatomical change. Rather than limiting analysis numeric outcomes, synthesized images yield interpretable and more informative visual representations that
"Equal contribution. Correspondence to: hc666 @ cam.ac..akk.k......

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support structured analyses and offer more actionable insights for clinical practice (Wu al., 2024; Chen et al., 2024; 2025).
Several methods have attempted to model discase progression. For instance, DiffuseMorph (Kim et al., 2022) introduces a morph field to describe pixel-wise displacements, and TADM (Litrico al., 2024) incorporates temporal awareness by predicting residual images conditioned age gaps. Despite these advances, generating temporally consistent and individualized disease trajectories re- mains an open problem. Beyond high-fidelity image synthesis, it is crucial for generative models to preserve fine-grained anatomical structures and accurately capture patient-specific dynamics. Al- though BrLP (Puglisi et al., 2024) takes step toward personalization by modeling volume changes, such guidance is coarse and provides only limited control over individualized trajectories.
Contributions: Motivated by these gaps. we propose a personalized generative framework for modeling disease progression based on flow matching. Our approach. termed Progression Latent Flow Matching (A-L.FM), is designed to generate trajectories at arbitrary future time points within a patient-specific latent space, ensuring temporal consisteney and clinical interpretability. The key contributions are summarized as follows:
We reformulate conventional flow matching, which typically models dynamics from t 0 to t 1, into formulation where the time variable explicitly encodes the future time gap. This extension transforms the horizon from a normalized range [0. 1] meaningful temporal range [0, 7], enabling prediction at arbitrary future time points T with consistent temporal semantics.
We introduce a patient-specific latent space, regularized by new ArcRank loss, which enforces chronology-awart alignment and captures individualized disease dynamics.
We show that the learned latent space supports interpretable visualization of patient trajectories. Notably, although disease severity is not used for training, the latent representations naturally reflect severity levels, providing clinically meaningful structure.
We further validate A-LFM on longitudinal MRI benchmarks and propose a pngression-specifie evaluation metric tailored to disease modeling called A-RMAE. Results demonstrate improved imaging fidelity and more accurate alignment with actual disease progression.
RELATED WORK
Generative models for disease progression. Generative modeling has emerged as a powerful strat- egy for simulating longitudinal disease changes. Farly efforts relied on generative adversarial net- works (GANs), either by introducing morphological priors to simulate aging effects (Ravi et al., 2019) by predicting deformation fields with 3D conditional GANs instead of direct intensity values (Ravi et al., 2022).
More recently. diffusion models (Ho al., 2020) have become the dominant paradigm due to their superior fidelity and stability. Extensions of this framework introduce temporal awareness and anatomical constraints. Sequence-Aware Diffusion Model (SADM) leverages multiple scans to autoregressively generate future MRIs (Yoon et al., 2023), while DiffuseMorph (Kim et al., 2022) produces smooth voxel-wise deformation fields across timepoints, thereby preserving topology. Pro- gressive Image Editing (PIE) (Liang et al., 2023) edits disease-related regions in medical images using text-guided diffusion models reflect how patient's 's condition evolves over time. Kyung et al. (Kyung et al., 2024) adopt electronic health records (EHRs), including medical history, to model temporal changes and enable medically meaningful generation. Temporally-Awee Aware Diffusion Model (TADM) conditions on age maps and adopts a residual prediction strategy, modeling progression as incremental changes rather than absolute reconstructions (Litrico et al., 2024).
Conditioning strategies further enhance subject specificity and anatomical fidelity. Brain Latent Progression (BrLP) employs ControlNet with volumetric ratio conditioning to synthesize individu- alized disease trajectories while integrating population priors (Puglisi et al., 2024; 2025). Similarly, BrainMRDiff fuses multiple structural masks (e.g., white matter, gray matter, ventricles) into a uni- fied conditioning representation, substantially improving anatomical realism (Bhattacharya et al., 2025). ImageFlowNet (Liu et al., 2025a) learns multiscale joint patient embeddings and position- parameterized neural flow fields to forecast full image-level trajectories.
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Latent Space
Image Loss
Patient Vector Z.:
2:1
Longitudina Order
Singlar Value E
LAX
SVD USV
ArcRank
ArcRank Loss
A-Latent Flow Matching
Forward Stochastic Flow (z) a.) + adw
Zj
Z
Stochastic Flow Manifold
Learned Deterministic Flow
A-LFM overview. A-LFM operates in the latent space. In the first stage, autoencoder constructs the latent space with ArcRank Loss to capture patient-specific disease trajectories, In the second stage, flow matching predicts disease progression along the trajectory over the total time horizon T' dtt where, for example, T = i, to adapt the actual prediction span rather than relying on fixed interval.
Figure 1:
In contrast these approaches, which primarily focus realism and population-informed pri- ors, our method targets patient-specific disease trajectories while explicitly modeling heterogeneity through a flow-matching generative framework.
Subject-level consistency and biomedical plausibility. Ensuring subject-specific consistency and biomedical plausibility is a central challenge in modeling synthetic disease progression. Early ap- proaches such as the Longitudinal Variational Autoencoder (Ramchandran et al., 2021) and Lon- gitudinal Self-Supervised Learning (LNE) (Zhao et al., 2021) focus on learning natient-tempora dynamics by constructing temporally coherent latent spaces, thereby producing individualized rep- resentations for downstream tasks.
Subsequent works introduced explicit mechanisms to regularize longitudinal consistency. Ren et al. (Ren et al., 2023) enforce subject-level coherence through local and multi-scale spatio-temporal features within self-supervised framework. In complementary direction, Treatment-Awan Diffu- sion (TaDiff) (Liu al., 2025b) incorporates prior scans and treatment information to jointly gener- ate future MRIs and tumor segmentations, thereby improving biological plausibility by conditioning on clinically relevant variables.
3 METHODOLOGY
Our proposed approach consists of two key components: (i) patient-specific latent learning via Ar- cRank (Sec. 3.2), and (ii) arbitrary-time progression modeling via A-LFM (Sec. 3.3).
Before delving into these components, we first present the preliminaries in Sec. 3.
3.1 PRELIMINARIES
Flow matching (Lipman et al., 2023; Tong et al., 2024) trains continuous normalizing flows by directly aligning vector fields instead of relying stochastic denoising objectives in diffusion models. Let no and ग denote the source and target distributions, respectively. Flow matching defines family of intermediate distributions (meeej)) along continuous trajectory connecting
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To and Tj. The goal is learn time-dependemt velocity field vg(x, such that the solution of the ordinary differential equation (ODE) (Lu et al., 2022) transports Ty exactly to T1 at t 1:
dxi dt
ug (),,
(1)
where the velocity field (x t) is trained to ensure that samples from To flow continuously into Tι-
Unlike score-based diffusion models, which approximate the score function Vx log गy (x( via noisy denoising objectives, flow matching bypasses score estimation by directly regressing the neural vector field (x, t) onto analytically known target fields. For example, under conditional flow matching (Lipman et al., 2023), one defines reference path (1 -t tx between samples Xg ~ To and X1 ~ Ti, yielding a target velocity
u² (X,, t) X1 Xo:
which is constant along the trajectory. The training objective then minimizes
(0) E Ex x1 t- (o. w1ll://ooooxxx o" (x,, e)
(3)
which yields stable training and ensures the learned flow recovers the correct marginal क at f = 1.
To further incorporate stochasticity (Albergo et al., 2023), the deterministic flow be extended to a stochastic differential equation the form
dz, v" (z+, di o dww,
where w, is a Wiener process and a controls the noise scale. This extension allows flow match- ing to model both deterministic transport and stochastic variability, providing greater flexibility in capturing complex data distributions.
3.2 ARCRANK: LONGITUDINAL ALIGNMENT OF PATIENT LATENT
To enhance sensitivity to patient-specific dynamics, we introduce a chronologically-aware latent representation learned via new contrastive objective, termed ArcRank Loss. This objective aligns representations across time for the same individual by enforcing both angular consistency and tem- poral ordering in the embedding space. Let denote the latent representation of an input extracted from a Variational Autoencoder (VAE) (Kingma & Welling, 2013) encoder E(-). The loss encour- ages
((z,) ((z,)
|z/1l
|zy|
ift, <t Z E Pk
(5)
where pk denotes the latent feature set of patient k, and / here represents the imaging capture time. Here, (-)) represents the direction of a latent vector, and || || is its magnitude. Intuitively, samples from the same patient are encouraged align along a consistent latent direction, while the trajectory respects chronological order (further along the trajectory corresponds to later disease stages).
In practice, extract these components via Singular Value Decomposition (SVD) (Klema & Laub, 1980) and write
|z|| Σ, where UEV SVD(z). where U captures the orientation (angle) and Σ encodes the scaling (norm).
Lz U,
(6)
AreRank Loss Computation. For a given patient k, let pk = [z1, 22, ... .2n) denote latent tn- We decompose each feature via SVD:
features times <
((z) Uz,
|| Σ,
The angular consistency loss encourages stability of feature orientations across time, while the tem- poral ranking loss enforces monotonic growth of feature magnitudes:
LATE
Σ IU. U
LRank
Σ
max (0, -EE -E)),,, bi
(8)
same patieut
same patient
where m > 0 is a margin hyperparameter. The final objective combines the two components:
LArcRank >aare Lan + Arank LRank,
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where Aree Arank balance the contributions.
In practice, the ranking term Caak tends to push timepoints for the same patient increasingly far apart, and the margin m is shared across all pairs (i,j), ic., it is not adaptively optimized for different temporal gaps. To mitigate this effect, we introduce an additional pull term that penalizes excessive separation in magnitude between temporally adjacent features:
L
b. E
(10)
We augment the ranking objective
RRnk
LRank Cpall;
(11)
using the same overall weight as LRank in the total loss. This pull term softly encourages consecutive timepoints to remain close latent space, while still allowing the hinge-based push term enforce the desired temporal ordering.
To stabilize training, for each pair (i.j) used in the AreRank loss, we apply the stop-gradies graddaaddennt oper- ator sg(.) to the representation of i.
3.3 A-LFM: FLOW MATCHING ALONG PATIENT TRAJECTORIES
While ArcRank enforces patient-specific chronological alignment, it does not explicitly capture how latent states evolve over time. To address this limitation, we introduce A-LFM, a flow-matching objective that learns smooth mappings across arbitrary time intervals within a patient's trajectory. Unlike standard flow matching. which interpolates between fixed source and target distributions (e.g., from + 1), A-LFM models temporal transitions on disease-specifie time scales T, where T denotes the future time relative to the baseline. For clarity, refer to the conventional [O, interval as Physical Sampling, and to our proposed [0, T formulation as Temporal Sampling-
Formally, given a patient k let 2,, z, denote paired latent states times f, st. We define the latent transition field (-).). parameterized by a neural network, which approximates the continuous- time velocity of latent dynamics. The goal is match this learned velocity field to the empirical difference between latent features across time:
0" (i,,)
2,
t ti
(12)
t, t
The associated flow-matching loss is then given by
LIOM())
(o((i v0 o(
(13)
Inference. Given input state state z, To predict the target state Xj at a later time t,, A-LFM integrates the learned velocity field forward in time. Specifically, fix discretization step size dt (e.g.. dt 0.01), that the total number of integration steps is
x, observed at time 4, the encoder maps it to latent representation
N
(14)
di
At each step, the latent state updated according to the learned dynamics
Zitdi
2; + dt uz(,, tz),
(15)
with time advanced as fitee t, dt. Repeated application of this update yields an approximation of the latent state at tj. which is then decoded to produce the predicted observation X,.
3.4 DISCUSSION
The use of Flow Matching. We use flow matching because it naturally models continuous tra- jectories while keeping intermediate states interpretable, which is crucial in our setting. It learns a continuous velocity field between observed endpoints and allows direct sampling of intermediate states, without relying on long numerical integrations. Compared to latent ODEs, this avoids sen- sitivity to ODE solver choices and reduces computational cost. While rectified flow methods are effective, they typically built diffusion trajectories; in contrast, flow matching gives a more direct and tractable formulation of the probability path that better aligned with our goal of faithful temporal interpolation.
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Grouna
DiflacKonhh
Figure 2: Method comparison. The first column shows the ground truth. All predictions initialized from the same baseline scan at age 71. Odd columns show predicted MRIs; even columns show residual maps relative the ground truth. Residuals use the magma colormap. scaled the 1st to 99th percentiles of the residual distribution, enhancing error visibility around the lateral ventricles (central autterfly-shaper region) and cortical gray matter (outer surface).
Latent-space trajectories reasoning. One central assumption in framework is that disease progression can be represented as a straight line in latent space, structured along a linear trajec- tory where the magnitude encodes disease stage and the direction preserves patient identity. While this design simplifies prediction, it raises an important question: can straight line adequately cap- ture both the shared and divergent aspects of disease dynamics across patients? We argue that this concern is valid. In our work, however, the linear trajectory is not intended to reproduce the full bio- logical complexity of disease, but rather to provide stable and interpretable scaffold that highlights the primary mode of variation corresponding to disease advancement.
Temporal uneven progression. We formulate flow matching (FM) over the interval [o, T). inter- preting the index as progression coordinate rather than physical clock time. However, although this formulation accounts for time differences, it implicitly assumes that progression is evenly dis- tributed along the disease trajectory. In practice, progression is often uneven: extended periods of stability may be punctuated by sudden changes, vice versa. The constant-velocity assumption in FM fails to capture this heterogeneity, effectively treating patient scans as uniformly spaced along the trajectory. To address this limitation, we introduce conditioning on the target time T together with sptient-specific attributes (e.g., sex, age, and clinical status) to enable the model to capture heterogeneous progression patterns that vary substantially over time.
Design details of ArcRank loss. The proposed ArcRank loss uses SVD to jointly capture the direction and magnitude of latent trajectories. Alternatives such as cosine similarity for angles and absolute values for magnitudes treat these aspects separately and can become unstable when latent features are noisy or vary in scale. In contrast, SVD provides an orthogonal basis in which singular vectors naturally describe trajectory directions and singular values represent their magnitudes. This unified representation is compact and numerically stable, allowing ArcRank loss to align trajectories along meaningful progression directions while penalizing inconsistent scaling.
EXPERIMENTS
4.1 EXPERIMENT SETTINGS
We build our study on three major Alzheimer's disease (AD) cohorts: ADNI (Petersen et al., 2010), OASIS-3 (LaMontagne et al., 2019), and AIBL (Ellis et al., 2009). Every MRI undergoes the same preprocessing pipeline: N4 bias correction (Tustison et al., 2010), skull stripping (Hoopes et al., 2022), resampling to 1.5 mm3 voxels. We then normalize tissue contrasts and register all scans to refined standard brain template. We random 80/5/15 split for train/validation/test..

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Table 1: Quantitative comparison of methods in terms of image quality metrics, including PSNR (dB) and SSIM (x1.0E2). Results are reported as mean + standard deviation. Type denotes the prediction strategy: "Direct" generates outputs directly, "Deform" estimates transformation field, "Noise" applies diffusion-based denoising, "ANoise" predicts and denoises progression residuals, and "AFlow" models progression through gradual residual prediction.
AINI
AIBI
OANIS
Method
Type
PSNR 1
SSIM 1
PSNR 1
SSIM
PSNR 1
SSIM
CadlaeAging (Campollo et all, 2022)
Direct
27.78 1: 1.49
92.04 0.99
28.41 2: 141
90.30
0.90
26.23 1.45
86.17 2.06
Counteryurth (Pombo et 2023)
1.31
28.96
92.10
26.79
1.42
DiffuseMarph et
1.63
93.57
29.17
92.70
28.
(Yoon 2023)
2.28
85.15
27,97
86.36
TADM (Litrico et al., 2024)
ANoise
27.89 1: 1,91
90.78 1.54
28.58
1.77
91.70
1,01
26.29 1.52
K5.51
1.93
ImagePlowNet (Lin et al., 2025aa
Flow
28.57 + 1.18
92.96 0.88
29.08
1.12
92.23
0.84
27.92
1.29
87.63 1.82
BiLP (Puglisi et al,, 2024)
Noise
28.51 4: 1.77
91.52
1.31
28.96
1.36
92.21
4: 0.97
27.98
1.40
87.93
1.44
ManhaConirol (Ying et ol., 2025a)
Noise
29.72 4: 1.04
93.60 0.96
29.86
1.21
93.17 1: 0.98
28. 24
1,28
K8,30
1.52
A-LFM (Ours)
AFlow
30.59 1: 0.89
94.62 0.85
30.52
1.03
93.92
0.88
29.01 1.19
89.36 1.29
We benchmark against a broad spectrum of recent approaches. Direct-prediction methods include CardiacAging (Campello et al., 2022) and CounterSynth (Pombo et al., 2023). Deformation-batt modeling represented by Morph (Kim et al., 2022). Diffusion-based methods span multiple variants: SADM (Yoon et al., 2023), which denoises full images; TADM (Litrico al., 2024), which denoises residuals; and two ControlNet-based (Zhang et al., 2023) models, BrLP (Puglisi al., 2024) and MambaControl (Yang et al., 2025a).
Metries. We evaluate reconstruction quality with two standard image-level metrics: Peak Signal- to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM). To capture anatomical fidelity, we followed BrLP (Puglisi et al., 2024) to report region-level mean absolute error (MAE) over clinically relevant structures (hippocampus, amygdala, lateral ventricles, cerebrospinal fluid (CSF), and thalamus).
However, measuring image similarity alone is insufficient the longitudinal setting. Scans from the same patient naturally exhibit high similarity because they share the same biological structure. The subtle deformations caused by disease are often small and easily overshadowed by the stable, unaffected anatomy. As a result, conventional metrics such as PSNR and SSIM tend to report inflated scores, failing to reflect clinically meaningful progression.
The true signal of interest lies in the residual differences between baseline and follow-up scans. These residuals often encode the disease trajectory. To capture this, we introduce a residual-based metric. Specifically, let
= Xo.
gen XT Xo.
(16)
where A denotes the residual image, and & denote ground- truth and generated MRIs, respectively. The metric is defined as the Residual-baat based Relative Mean Absolute Error (A ARMAE)):
Agr A gen
A A-RMAE
(17)
[ gt + (Agon))
By definition, A-RMAE E [0, 2). A smaller value indicates that the predicted residual aligns with the ground-truth residual, i.e., the model has correctly captured disease-relevant evolution. If the model predicts almost no change (essentially copying the baseline image), then Agen > 0. In this case, both numerator and denominator are dominated by /Agel. and the score approaches 2. Likewise, the prediction deviates strongly, A gen dominates, again driving the score toward 2.
4.2 BENCHIARK COMPARISONS
We present qualitative results in Figure 2. In this subject, disease progression primarily affects the lateral ventricles (the central outterfly-shaper region) and the cortical gray matter (outer surface). SADM, TADM, and MambaControl fail to capture changes in the lateral ventricles, resulting in pronounced butterfly-shape error in the residual image. DiffuseMorph and BrLP better capture ventricular changes, but leave substantial residuals along the cortical surface. Our method also
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Table 2: Quantitative comparison results on clinical structure faithfulness metries are reported in region-based MAE and A-RMAE residual-based Relative Mean Absolute Error). Results are re- ported as mean + standard deviation.
Method
Type
ADNI
AIBL
OASIS
Region MAE
A-RMAB
Region MAB
R-RMAE
Region MAE
3-RMAB
CurdiacAging (Cumpello 2022)
Direct
0.289 0.33
0:771 1 0.12
0.281 1 0.35
0.698 0.12
0.345 0.35
0.739 0.13
CounterSyath (Pombo et al, 2023)
Direct
0.272 = 0.32
0.704 = 0.11
0:256 +: 0.30
0 0.12
0.298 0.34
0,000 0.12
DittuseMophh (Kim al., 2022)
Deform
0.250 0.28
0.516 + 0.10
0.226 + 0.27
0,482 0.10
0.279 0.29
0.503 0.11
SADM (Yoon 2023)
Noise
0.30
0.693 0.12
0.365
TADM (Litrico al,, 20124)
ANosse
0.203
0.11
0:243 0.30
0.684 0.11
0.291
0.83
ImsgeFloweee (L.u et al, 2025a)
Flow
0.259 0.30
0.589 + 0.11
0.240 + 0.29
0.561 0.12
0.263 0.32
0.574 0.12
Bef (Puglisi all, 2024)
Noise
0.257 0.32
0.630 + 0.10
0.278 + 0.31
0.594 0.11
0,333 0.36
0.622 0.11
MambuControl (Ying et all,, 2025s)
Noise
0.225 0.30
0.554 1: 0.09
0.349 0.30
0.525 0.10
0.299 0.32
0.561 0.10
A-IFM (Ours)
AFkkww
0.28
0.08
0.276 0.29
0.417 0.10
0.262
0.473
Ablation study results (mean across datasets). We evaluate the effect of different auto- encoder training strategies (Are Loss, Rank Loss, AreRank Loss) and flow-matching manifold sam-
Table 3:
pling strategies ((0, 1] vs. [0, T). The Cond. represent using condition or not. The row with gray background indicated the proposed method.
Imsaee Quality
Strueture Fidelity
Model
Anto-Enewder
FM Sampling
Cond.
PSNR 1
Region MAE
4 4-RMAE
LFM (Baselinc)
[0. 1
27.59
1.78
88.62 1.63
0.357 0,342
0.146
Conditional LFM
[0. 1
28/16 1.22
1.15
0.299 0.312
0.101
[0. T1
28.78
90.97 1.07
0.286 0,295
[0. 1
92.38 0.95
0.282
A-LFM
Rank Loss
10.
28.36
91.15 1.11
0.272 0.285
0.474 0.088
ArcRank Loss
[0.
92.74
0.9
01243 0.277
ArzRank Loss
10.
30,04
1.04
92.63 1.03
0.233 0.282
0.442 0.087
shows error in the ventricles; however, these are less intense, with thinner boundaries and smaller cortical-surface errors, demonstrating improved overall accuracy.
We report PSNR and SSIM Table and Region MAE together with A-RMAE in Table 2. Across all three datasets, our proposed A- consistently achieves high performance.
In Table 1, A-LFM improves PSNR by a clear margin over the strongest baseline. On ADNI, it reaches 30.59 dB, exceeding the second-best method (MambaControl, 29.72 dB) by +0.87 dB. Similar gains are observed on AIBL (+0.66 dB) and OASIS (+0.77 dB). The SSIM results mirror this trend: A-LFM achieves 94.62, 93.92, and 89.36, improving upon the best baselines by roughly +1.0, +0.7, and +1.1 points, respectively. These consistent improvements indicate that A-LFM produces reconstructions with both higher fidelity and sharper structural alignment.
Table 2 further validates these observations with volumetric error metrics. A-LFM yields the low- est Region MAE on ADNI (0.210) and OASIS (0.262), and matches the best-performing method (DiffuseMorph) on AIBL (0.226). More importantly, it achieves the lowest A A-RMAE across all datasets: 0.436 on ADNI, 0.417 on AIBL, and 0.473 on OASIS. Compared to the strongest baseline (MambaControl), this represents relative error reductions of about 21 21%,2 21%, and 16%, respectively.
4.3 ABLATION STUDY
We provide visualization results of the learned latent space in Figure 3 on test cases in ADNI dataset, where t-SNE is used to project the representations into two dimensions. As shown in the left panel, the latent trajectories of individual patients are well aligned. Interestingly, the right panel reveals that the latent space also organizes according to diagnostic status, despite the fact that this information was never used during training.
To assess the contribution of each component in framework, conducted ablation study across three datasets, as summarized in Table 3. The experiments examine the effect of (i) intro- ducing conditional information, (ii) different auto-encoder training strategies (Are Loss, Rank Loss,
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(a) colored by patient identity
(b) colored by diagnosis status
Figure 3: t-SNE projection of the learned longitudinal latent space into two dimensions. Coloring by subject ID shows that scans from the same patient cluster together. (b) Coloring by disease status shows that seans with the same diagnosis are grouped closely. CN: Cognitively Normal. MCI: Mild Cognitive impairment. AD: Alzheimer's Disease (Dementia Stage).
Table 4: Ablation on the proposed components.
Angular loss
Ranking loss
Sampling
PSNR
SSIM
Arc Loss
0, 7
29.88
92.31
Rank Loss
0, T
28.85
91.10
Cosine Similarity
0,
29.13
91.10
Cosine Similarity
Simple Rank Loss Simple Rank Loss
0,
28.32
89.92
Arc Loss
0. 28.44
89.87
ArcRank Loss), and (iii) different flow- now-matching (FM) manifold sampling strategies, namely physi- cal sampling [0, 1] versus temporal progression modeling [0, T).
The baseline Latent Flow Matching (LFM) (Dao et al., 2023) model without conditioning performs the worst across all metrics, showing notably low SSIM/PSNR and high error values. Incorporating conditional information (Conditional LFM) significantly improves image quality (SSIM from 88.62 to 91,20; PSNR from 27.59 to 28.46) and reduces both Region MAE and A-RMAF.
Within the A-LFM ablation, observe has direct impact: using Are Loss alone yields clear improvements, whereas Rank Loss alone slightly undermines performance. This is because Arc Loss encourages patient trajectories to follow a meaningful direction, while Rank Loss without Are imposes only a weak magnitude constraint. In contrast, their combination (ArcRank Loss) achieves the best balance, suggesting that structural alignment (Arc) and temporal ordering (Rank) are complementary. Second, extending the FM sam- pling strategy from [0, 1] [0, further improves results by promoting gradual residual modeling over meaningful temporal intervals.
consistent trends. First, the choice of loss function
Finally, we visualize qualitative progression predictions in Figure 4 using cases from three datasets, demonstrating the ability of A-LFM to predict timepoints at arbitrary intervals. The results show disease-related deformations primarily affecting the ventricles and surrounding cortical areas, which is consistent with clinical observations.
future
We present qualitative visualizations of predicted disease progression in Figure Each row il- lustrates disease trajectories nine years generated by A-LFM. The intermediate steps provide clinically interpretable insights into the progression process, capturing characteristic neurodegen- erative patterns such ventricular enlargement and cortical thinning in the temporal and parietal regions. These deformations align with established clinical observations, underscoring the biologi- cal plausibility of our model.
To further verify each proposed component, we provide additional ablations Table We evaluate cosine similarity Leusine surrogate for Are loss and simple ranking loss Simple surrogate

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Published as a conference paper at ICLR 2026
ADNI
ATBL
OASIS
Time
Year
Year
2 Year
Year
Year
5 Year
Year
Year
Year
9 Year
Figure 4: Continuous disease trajectory predicted by A-LFM at one-year intervals. Odd rows show the baseline MRI (year 0) and predicted MRIs from years 1 1-9; even show residual maps relative to baseline. Progression highlights structural abnormalities, primarily in atrophy-related regions (e.g., hippocampus, ventricles, surrounding cortex).
for Rank loss, defined as follows:
(, Zz)
Ccosine (c.))no(t..)
-i.j)=1- =1
Ssimple (i.5) max(0, dj dz).
(18)
|z |zy11'
Cosine similarity performs slightly global angular alignment and does not capture the fine-grained latent directional structure modeled by Are loss. contrast, the simple rank loss without a margin often leads latent mode collapse, explaining its poor performance when combined with either Arc loss or cosine similarity.
than Are loss, which is expected since it only enforces
Loss Weight. Auro relatively sensitive. Values Amre > 0.01 consistently cause collapse, while 0.0025-0.0075 are stable across runs, with Aure 0.0075 noticeably degrading AE reconstruction. We therefore set Amn = 0.005 as a compromise, trading a small decrease in AE reconstruction for improved flow-matching performance (+0.44 PSNR over 0.0025).
For Aank, values above 0.05 hinder convergence, whereas the range 0.005-0.00 yields similar be- havior. We choose >rank 0.01, which gives slight PSNR gain (+0.055..
Speed Analysis AreRank involves an SVD operation, which is computational expensive. prac- tice, we use torch. www.lg..nsel...............m (z, hallmmatrices-ei
which gives 6 speedup compared the full matrices variant (0.0552s - 0.0092s on average over 50 runs). Overall, Ar- cRank increases AE training time by 40% (1.4x), which we regard as a reasonable overhead given the resulting performance gains.
5 CONCLUSION
We introduce Progression Latent Flow Matching (A-LFM), framework that unifies the proposed ArcRank loss with temporal flow matching to capture patient-specific disease trajectories. To evalu- ate progression in isolation, propose new metric, A-RMAE. On longitudinal MRI benchmarks, A-LFM consistently achieves higher fidelity, lower error, and tighter alignment with ground-truth progression than prior methods. Beyond accuracy, yields temporally coherent and clinically in- terpretable trajectories. These results show that A-LFM provides a new direction for progression modeling, with the potential to generalize across other temporal generation tasks.
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Appendix
A TRAINING SETTING
We adopt the AdamW optimizer (Loshchilov & Hutter, 2017) for all experiments. For the autoen- coder (AE) and 3D U-Net (Ronneberger et al., 2015), we trained with learning rate of x 10-3 and batch size of 2 for 300 epochs. For the flow matching model based on the 3D U-Net, we used a reduced learning rate of 3 x 10 with a larger batch size of 4 for 200 epochs.
B CONDITIONAL GENERATION
Following Litrico et al. (Litrico et al., 2024), we encode the current sample time in flow matching into continuous embeddings using sinusoidal positional encodings. These time embeddings act as an additive bias to the input, ensuring that the generative process is aware of its temporal position.
Building this, and inspired by BrLP (Puglisi al., 2024), we introduce explicit control signals that combine patient-specific attributes with temporal queries. In particular, we condition the model not only on the start time, the current sample time, and the end query time, but also on the pa- tient attributes. This design enables the model to incorporate both subject-specific and task-specific information when shaping the generative trajectory.
To inject these conditional signals into the U-Net backbone, we explored three strategies: (1) Ad- ditive biasing, (2) Cross-attention (Vaswani al., 2017) and (3) Adaptive Layer Normalization
(AdaLN) (Raffel et al., 2020).
Among these approaches, our experiments show that AdaLN is most effective with our temporal sampling over the interval T). It adapts the network representation in temporally aware and context-sensitive manner, allowing the generative process be steered smoothly by patient attributes and target query times.
The implementation AdaLN is realized through an initial one-layer MI.P that processes the condi- tion signals, followed by additional MLPs at each U-Net decoder layer to generate the corresponding AdaLN modulation parameters.
C AUTO-ENCODER ABLATION
Table 5 summarizes the effect of AE capacity and training crop size. For the capacity ablation, we vary the encoder channels while fixing the crop size to 643, For the crop-size ablation, fix the AE to [64, 128, 256] and compare 483 vs. 643 crops.
Table 5: Ablation on AE capacity and training crop size.
AE capacity (crop 64")
Crop (AE [64, 128, 256))
Channels
PSNR
SSIM
Crop
PSNR
SSIM
661, 128, 256)
30.04
92.63
611
30.04
92.63
64, 128, 128
29.89
92.55
483
91.71
128)
29.62
92.10
We do not use deeper or wider AEs, as these configurations lead to out-of-memory (OOM) errors on our RTX A6000 GPU (48 GB). Based on the above results, we use channels [64, 128, 256) and crop size 6 as default configuration. Larger crops (e.g., 723) also result in OOM on hardware. To keep the comparison with baselines fair, we do not use a pretrained AE, although initializing with MAISI (Guo et al., 2025) can further improve PSNR (from 30.04 31.97 for [64, 128, 256)).
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Table 6: Quantitative results across different prediction horizons (years into the future). Measure- ments are reported using PSNR (dB), SSIM (x 1.0E2), Region MAE, and A-RMAE.
Yeur
PSNR 1
SSIM
Region MAB
A-RMAE 4
1
31.61 + 0.87
93.08 = 0.75
0.209 0.107
0.386 0.107
2
31.79 + 0.92
93.79 = 0.77
0.217 + 0.106
0.309 + 0.097
3
31.09 + 0.95
93.51 = 0.82
0.206 + 0.118
0.388 + 0.089
32.48 + 0.93
93.95 + 0.89
0.201 0.132
0.395 0.084
5
32.14 1:
93.59 +:
0.148
0.405
6
31.37 +: 1.02
93.07 - 0.95
0.221
0.414 0.081
7
30.12 + 0.98
92.58 = 1.07
0.241 + 0.176
0.436 + 0.082
8
29 83 + 1.05
92.18 1.15
0.261 0.191
0.459 + 0.089
9
28 +: 1.07
90.65 = 1.20
0,279 1
0.487 0.085
10
1.23
91.11 1.37
0.302 0.246
0.652 0.104
11
28.71 + 1.13
91.32 1.22
0.294 - 0.218
0.506 + 0.094
13
26.98 + 1.29
89.96 = 1.44
0.339 + 0.259
0.579 + 0.109
D LONGITUDINAL PROGRESSION QUANTITATIVE RESULTS
Table 6 summarizes predictive performance across different future horizons. For short- mid-term forecasts (I-5 years), reconstruction metrics remain consistently high: PSNR hovers around 31- 32 dB and SSIM above 93%, indicating strong fidelity reproducing structural details. Region MAE is also relatively stable in this range (~ 0.20), suggesting reliable local accuracy, while A- RMAE values remain below 0.41, reflecting well- well-preserved progression dynamics.
Beyond 6 years, however, all metrics exhibit gradual degradation. PSNR and SSIM decline steadily, dropping to 28 dB and below 91% by year 10, and further to 26.98 dB 89.96% at year 13. Con- currently, Region MAE and A-RMAE increase monotonically, indicating that both absolute errors in regional values and their temporal progression deviate more strongly with longer horizons. No- tably, the sharp rise in A-RMAE after year 10 (> 0.50) highlights growing difficulty in capturing long-term progression trends.
We also observe that the prediction trend is not strictly linear the prediction horizon increases. This mainly because different time horizons are estimated from different subsets of subjects. In particular, fewer subjects have follow-up data at 10-13 years compared to 1-5 years, which introduces higher variability and heterogeneity, leading to slightly inconsistent trends.
E ON THE STABILITY OF A-RMAE
Residual-based metrics such as A-RMAE can in principle be affected by imperfect registration and intensity inhomogeneity, and preprocessing cannot guarantee perfectly aligned, bias-free images. Here we analyze how such imperfections influence the metric.
In our setting, A-RMAE is defined voxel-wise
Agr A gen
A-RMAE
(19)
7 [
g1 + A
so that A-RMAE E [0, with values close to 2 indicating large disagreement between the two residuals. We model misregistration and residual bias-field effects as an additive perturbation Amis on the ground-truth residual, yielding
Amis + Agt
A gen
A A-RMAE
(20)
1 [|Amis mis + Agi
+ /A gen
When Amis is small relative to Agt and Agen numerator and denominator are perturbed a compa- rable way, A-RMAEmmss remains close to the ideal A-RMAE. As Amis increases, the main effect a mild compression of the dynamic range (the effective upper bound becomes slightly below 2), rather than systematic bias toward any particular model.
To quantify this effect, we perform simple sensitivity analysis by adding Gaussian noise with standard deviation the residuals and recomputing A-RMAF. Table 7 reports the mean, standard
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Table 7: Sensitivity of A-RMAE additive Gaussian noise on the residuals.
(noise)
Mcan A-RMAE
Standard Deviation
Bias vs. True
0.00
2,000000
0.000000
0,000000
0.05
1,999842
0.002315
-0.000158
0.10
1,999375
0,005982
-0.000625
0.15
1,99214
0.01 0.011430
786
0.20
1996102
0.019752
-0,003898
0.25
1.99994
0.031245
-0.007006
0.30
1.991224 24
0.046521
-0.010876
0.35
1983612
0.0642 10
00011388
0.40
1.976348
0,085402
-0.023652
0.45
1.968400
007978
-0.031260
0.50
1.902255
0.1330
-0.039745
0.55
1.950492
1618088
-0,049508
0.60
1.939101
0.191156
-0.060899
0.65
1.926345
0.222974
-0.073655
0.70
1,9118900
0,255780
-0.088100
0.75
1.892232
0,288901
-0.103768
0.80
1.879110
0.322410
-0.120890
0.85
1.861775
0,355122
-0.138225
0.90
1.843569
0,386230
-0.156431
0.95
1.834021
0.415104
-0.165979
1.00
1.826570
0.462351
-0.173430
deviation, and bias relative to the noiseless value (2.0). Even for relatively large noise levels (a up to 1.0), the induced bias remains small compared the full range [0, 2]. supporting the robustness of A-RMAE to moderate misregistration.
F CLINICAL CONDITIONING, SETUP AND VERIFICATION
We conduct series of analyses to assess the robustness of the model to perturbations in the condi- tioning metadata.
Age. Age serves the temporal anchor for longitudinal prediction, future timepoints de- fined by (baseline age + time span). Injecting noise into age would therefore shift the implied prediction timepoint, that the generated image no longer corresponds to meaningful clinical follow-up. Such an ablation would be difficult to interpret, and for this reason we do not treat age as noise-robust attribute.
Sex. To evaluate robustness with respect to sex, we intentionally flipped the sex attribute and re-evaluated the model. On ADNI, performance changed only marginally, from PSNR/SSIM of 00..9/944.66 to 30. 12/94.47, indicating limited sensitivity to this source of label noise.
Clinical status. clinical practice, diagnostic labels are inherently noisy. To reflect this, we inject Gaussian noise into the clinical status during training model diagnostic uncertainty. Specifically, we use zero-meat Gaussian noise with standard deviation equal to one-third of the status class interval (interval = 3).
Under perturbed status labels, performance remains reasonable, with PSNR/SSIM degrading only slightly from 30.59/94. /94662 to 20.81/93, /93.58, demonstrating robustness clinically realistic label noise.
G LIMITATIONS
Our work, while demonstrating the potential latent flow matching for longitudinal imaging gen- eration, has several limitations that we wish to acknowledge.
Task-specific limitation. In the current study, we restrict our focus to AD, which provides one of the most widely available longitudinal imaging datasets in the medical domain. This restriction is
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Published as a conference paper at ICLR 2026
pragmatic, AD offers abundant imaging data suitable for model training and evaluation. How- ever, inevitably narrows the generalizability our findings. future work, we aim to extend framework to other progressive diseases such brain tumors, where longitudinal imaging car- ries unique challenges, including rapid progression patterns, heterogeneous lesion appearance, and treatment-induced alterations. Moreover, encourage exploration of our method beyond medical imaging, where modeling temporal dynamics may shed light on broader scientific and engineering problems.
Dataset processing limitation. Although we followed standard MRI preprocessing protocols, vari- ations across scanners and acquisition protocols introduce substantial heterogeneity the data. Such differences may affect the stability of model training and the reliability of generated outputs, Fur- thermore, we identified occasional metadata inconsistencies (e.g., mislabeling of imaging orienta- tion), which led to registration failures in certain cases. While these issues were infrequent, they highlight the importance of rigorous data curation and quality control in longitudinal imaging re- search. Future work may benefit from harmonization techniques scanner-invariant representations to further mitigate such variability.
H FUTURE WORK
future research, we plan to enrich our framework in several important directions.
First, the incorporation of explicit anatomical information could enable more fine-grained modeling of disease progression. By constraining generation with structure-awars priors (c.g.. hippocampus, ventricles, cortical regions), the model may better capture local pathological changes while preserv- ing biological plausibility.
Second, beyond modeling each patient in isolation, future work may explore leveraging inter-patien disease trend similarity and dissimilarity. Identifying cohorts of patients with comparable progres- sion patterns may enable transfer of knowledge across individuals, while simultaneously capturing unique patient-specific deviations. In addition, modeling nonlinear progression dynamics remains an important direction for future work.
Addressing dataset heterogeneity remains another critical challenge. Future works may investigate harmonization techniques and scanner-invariant representations to mitigate variability introduced by different acquisition protocols and hardware. Such advances will be essential for scaling the framework large, multi-center cohorts and for ensuring robust generalization in real-world clinical applications.
I DISCUSSION OF LLM USAGE
We used large language models (LLMs), including ChatGPT (OpenAI, 2023) and Gemini (Team al., 2023), as writing assistants for grammar correction and style refinement. All technical content, methodology, and experiments were developed by the authors.
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Reviews:
[{"review_id": "Pk4ny1aSNY", "reviewer": "Reviewer_TJiN", "summary": "The paper proposed a latent flow matching method for disease progression prediction. The key idea is to enforce monotonic, per-patient latent progressions (same direction, growing magnitude) and then learn a temporally meaningful velocity field in latent space, so progression becomes smoother and clinically interpretable. They evaluate the method on ADNI, AIBL, OASIS-3.", "questions": "See weaknesses for details.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 1, "strengths": "- The paper has a clear formulation that couples patient-specific latent alignment (ArcRank) with temporal flow matching.\n\n- The method shows consistent empirical results across three longitudinal AD MRI benchmarks.\n\n- The paper has good ablation and visualization.", "weaknesses": "- Temporal sampling [0, T] still effectively assumes roughly uniform progression between scans; the paper acknowledges uneven progression but does not truly model accelerations/plateaus.\n\n- Evaluation is confined to AD-style neurodegeneration datasets; claims about general utility (tumor, faster diseases, multi-organ) are speculative. It strongly weakens the conclusion.\n\n- ArcRank depends on SVD-based decomposition per latent, which could be brittle or expensive and the paper does not compare to simpler angular/ranking surrogates on equal footing.\n\n- The method hinges on a learned AE latent; there is no analysis of how sensitive results are to the AE capacity or to using a stronger/pretrained encoder.\n\n- The new metric is reasonable but mostly motivated empirically; there is no user/clinician study to show that better ∆-RMAE corresponds to more actionable longitudinal reads. If a disease progression does not have user study from medical doctors, it is not convincing to clinical readers.\n\n- Clinical conditioning is mentioned (age, sex, status) but not deeply analyzed—no ablation on which attribute matters most, or on robustness to missing/noisy metadata.\n\n- Many important previous works are not mentioned and compared, such as [1,2].\n\n\n[1] Kyung, Daeun, et al. \"Towards Predicting Temporal Changes in a Patient's Chest X-ray Images based on Electronic Health Records.\" arXiv preprint arXiv:2409.07012 (2024).      \n[2] Liang, Kaizhao, et al. \"Pie: Simulating disease progression via progressive image editing.\" (2023).", "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": "gCRulN5fkt", "reviewer": "Reviewer_dApu", "summary": "This paper introduces a generative framework for modeling patient-specific disease progression from longitudinal MRI data. The authors treat the disease dynamic as as a velocity field and use ideas from flow matching to align the temporal evolution of patient data. To overcome the mismatch of representations between patient-specific trajectories and the latent space representations, they propose to learn patient-specific latent alignments. These alignments are penalized by a definition of a new loss, what is introduced here as a ArcRank loss. This loss measures the discrepancies between both representations by aligning latent trajectories across time within patients and by enforcing angular consistency and monotonic magnitude growth. This loss is optimized under a temporal flow-matching framework (that has been proposed before) to learn continuous velocity fields over arbitrary time intervals. The authors claim that the combination of this approach enables the learning of personalized disease progression as smooth latent flows. Experimental results are demonstrated on ADNI, AIBL, and OASIS-3 datasets with the image fidelity (PSNR/SSIM) and anatomical progression accuracy as metrics for evaluation.", "questions": "What is pull and push in Figure 1 in the ArcRank loss panel?\n\nCan the authors comment on the computational efficiency of the ArkRank loss?\n\nAre the weights \\lambda_{arc} and \\lambda_{rank} fixed or learnt over time? How are they chosen?\n\nCan the authors comment on the stability of the ArkRank loss? \n\nIn the ablation study (Table 3), how will the w/ Arc loss over [0, T] and the Rank loss over [0, T] perform? This may yield more granular information when the full w/ Arc+Rank loss is evaluated over [0, T]. \n\nIn Figure 4, why do you see more progression prediction (enlargement of ventricles) in the ADNI dataset over AIBL and OASIS? Are the cases more severe in ADNI compared to the other two datasets?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "While different elements (TADM, BrLP, SADM etc., which are cited here) used in this work have been previously proposed separately, one of the contributions of this paper is to combine these several ideas into a common framework. This makes this work somewhat novel.\n\nThe main novelty of the work is the introduction of the matching loss ArkRank loss. This loss enforces patient-specific trajectory alignment and temporal ordering. The trajectory alignment is achieved using angle matching of features in the latent space, while the monotonic growth of time features is achieved by temporal ordering (ranking).\n\nAnother contributions is the reformulation of flow matching by extending the sampling strategy from a fixed unit interval to an arbitrary interval. This improves the accuracy and minimizes residual errors, especially with arbitrary time-domain patient samples. \n\nExperimental evaluations over multiple datasets is a strength. \n\nThe close clustering of patient identity as well as diagnosis status helps demonstrate the interpretability of the method. The authors also qualitatively demonstrate MRI progression over 9 years. \n\nAblation studies are performed adequately.", "weaknesses": "There is one main novel idea in the paper, i.e. the introduction of the ArcRank loss. The rest of the ideas are incrementally novel and have been conceptually proposed before and also applied to MRI images. \n\nThe ArcRank loss involves an SVD may be expensive to evaluate. \n\nAn intrinsic weakness in the definition of the ArcRank loss is the reliance on two  weights \\lambda_{arc} and \\lambda_{rank}. The authors don't mention how these weights are imposed. Aligning the directions (first term) and maintaining the ordering (second term) is a non-trivial problem, even when the trajectories or the initial and final mappings are known. Thus the computation of the loss is itself challenging. Since the loss function is supposed to be on of the main novel contributions, it should be further analyzed. \n\nThe ablation studies with the Ark loss, Rank loss, Ark + Rank loss don't seem to show dramatic improvement in results. Although the role of the arbitrary sampling scheme over [0, T] may be important. This is not fully discussed.", "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": "jFfhOvGH8T", "reviewer": "Reviewer_CqTg", "summary": "The authors point out a key limitation of current methods for modeling (intrinsically continuous) disease progression: the latent representations are often scattered, lacking semantic structure, and diffusion-based models disrupt continuity with random denoising process. To remedy this, the authors propose to treat the disease dynamic as a velocity field and leverage flow matching to align the temporal evolution of patient data. To ensure the latent space is organized by clinical severity, he authors propose to learn patient-specific latent alignment that enforces patient trajectories to lie along a specific axis along which clinical severity monotonically increases. The proposed method, termed $\\Delta$-LFM, demonstrates stronger empirical performance and offers a way to interpret and visualize disease dynamics.", "questions": "1. Please refer to the weaknesses.\n2. Please also refer to the minor formatting suggestions in the strength section. These are just suggestions but not mandatory.\n3. In Table 3, I believe SSIM and PSNR are swapped.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. I find this topic computationally interesting, scientifically important, and clinically relevant.\n\n2. The proposed method is well motivated and easy to follow. \n\n3. Very good visual presentation. \n\n    a. The figures are beautifully made, with carefully chosen colors (Figure 1), clear illustration of ideas (Figure 1), and proper colormaps (Figures 2 & 4). The only less nice-looking figure (Figure 3) can be easily improved by removing top and right borders and enlarging the labels and tick labels.\n\n    b. Tables are also well designed and easy to follow. My only suggestions are to remove the vertical lines and adjust the column spacing or put a categorical name on top if you want to further distinguish the columns. For example, for Table 3, you can consider something like “image quality” above “SSIM” and “PSNR”, and “clinical structure faithfulness” above “Regional MAE” and “$\\Delta$-RMAE”. Besides, you can use \\cmidrule(lr){startColumn – endColumn} for the horizontal bars below each dataset name to make sure consecutive horizontal bars are not touching.\n\n4. Quantitative results look promising. Approximately 1.0 absolute point increase in PSNR and SSIMx1E2 are shown across three large-scale datasets.\n\n5. Ablation results are comprehensive and properly showcase the effectiveness of the proposed ArcRank loss.", "weaknesses": "1. A few comments on comparisons to existing work.\n\n    a. The authors mentioned that the proposed method “treats the disease dynamic as a velocity field” when modeling disease progression. As a result, I believe it is expected to compare against ImageFlowNet [1], since the design philosophy is similar. The authors can stay assured that I recognize the novelty of this submission, since there are sufficient distinctions, namely (1) flow matching instead of neural differential equations and (2) the ArcRank alignment.\n\n    b. I am also aware of a recent work [2] that uses flow matching for disease progression in longitudinal images, but comparison against it will be an unreasonable request, because it is too recent (Oct 2025) and the code is not available.\n\n2. For methods that forecasts longitudinal images, one major concern I have is that they tend to overly reconstructing and minimally forecasting. A common shortcoming I observe in this field is the underestimation of changes in the images over time. In this paper, the authors have not sufficiently shown that the proposed method is not simply performing very good reconstruction of the input image. For example, in Table 4 in appendix, the authors showed the forecasting performance degrades as the time horizon increases, but that could also be explained by an alternative hypothesis that the prediction is just a reconstruction of the input. I would like to see how the authors can argue against my concern.\n\n[1] ImageFlowNet: Forecasting Multiscale Image-Level Trajectories of Disease Progression with Irregularly-Sampled Longitudinal Medical Images, ICASSP 2025 Oral.\n\n[2] Longitudinal Flow Matching for Trajectory Modeling, arXiv 2025.", "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": "bTFoC5QkJJ", "reviewer": "Reviewer_UdDj", "summary": "The research team introduces $\\Delta$-LFM for longitudinal MRI modeling that learns patient-specific disease trajectories as continuous latent flows. They focus on the problem of patient-specific trajectory generation, which is currently a very valuable topic in the field, as most of the past models focus on population-level prediction. Specifically, to address this problem, the paper suggests a new loss: ArcRank Loss in the latent space to guide the patient-specific disease trajectories to have a stable direction and monotonic disease progression. The team also provides a temporal flow matching ($\\Delta$-LFM architecture, which generalizes flow matching to clinically meaningful intervals $[0, T]$ for arbitrary future-time predictions.  Besides the novelty in the model itself, this paper also suggests a new metric, $\\Delta$-RMAE, which aims to capture the residual differences between baseline and follow-up scans. \n\nThe authors utilize three datasets: ADNI, OASIS-3, and AIBL to validate their model's performance. $\\Delta$-LFM outperforms direct-prediction, deformation, and diffusion baselines (e.g., DiffuseMorph, TADM, BrLP, MambaControl) while producing interpretable patient-specific latent trajectories.", "questions": "Same as weakness.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. Clinical relevance and motivation. The focus on individualized disease dynamics—rather than population-level progression—is well motivated and important for neurodegenerative modeling.\n2. Coherent methodology. Combining flow-matching dynamics with a longitudinal latent regularizer (ArcRank) yields interpretable and temporally smooth trajectories.\n3. Elegant SVD-based alignment. Treating each patient’s latent tensor $Z_k$ as a matrix and applying SVD to extract orthogonal direction (U) and magnitude ($\\sum{}$) is a neat, principled idea that mitigates the instability of cosine-norm losses under noisy or scale-varying latents.\n4. Robust experimental design. Evaluation on three large AD cohorts with multiple baseline classes (direct/deformation/diffusion) is comprehensive; ablations are clear and interpretable.\n5. New progression metric ($\\Delta$-RMAE). Correctly highlights that PSNR/SSIM can mask small but clinically meaningful anatomical changes.\n6. Interpretability. Latent trajectories align by patient and even cluster by diagnosis despite no supervision—visually persuasive evidence that ArcRank captures disease semantics.", "weaknesses": "1. $\\Delta$-LFM’s formulation closely parallels latent-ODE and rectified-flow approaches. The paper should more clearly delineate the conceptual or practical advantages of its flow-matching objective over these established continuous-dynamics frameworks.\n2. The model assumes straight-line latent trajectories and roughly constant velocity; though acknowledged, this remains biologically limiting. More details on how conditioning on T and patient attributes relaxes this assumption would help. \n3. $\\Delta$-RMAE relies on image residuals, which are potentially confounded by registration or intensity artifacts. A sensitivity analysis to misregistration/bias correction would increase confidence.\n4. The authors claim that SVD is better than cosine similarity and absolute values for magnitudes, but there is no direct comparison between the performance of these two designs. It will be better if the authors could provide a comparison between them.", "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)