CRONOS: Continuous time reconstruction for 4D medical longitudinal series
Authors: Nico Disch
Saikat Roy
Constantin Ulrich
Yannick Kirchhoff
Maximilian Rouven Rokuss
Robin Peretzke
David Zimmerer
Klaus Maier-Hein
Venue: ICLR 2026 Poster (2026)
Keywords: Medical Imaging
Flow Matching Longitudinal
Spatio-Temporal
Trajectory Learning
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: Continuous time reconstruction for 4D medical longitudinal series

Abstract: Forecasting how 3D medical scans evolve along time is important for disease progression, treatment planning, and developmental assessment. Yet existing models either rely on a single prior scan, fixed grid times, or target global labels, which limits voxel-level forecasting under irregular sampling. We present CRONOS, a unified framework for many-to-one prediction from multiple past scans that supports both discrete (grid-based) and continuous (real-valued) timestamps in one model, to the best of our knowledge the first to achieve continuous sequence-to-image forecasting for 3D medical data. CRONOS learns a spatio-temporal velocity field that transports context volumes toward a target volume at an arbitrary time, while operating directly in 3D voxel space. Across three public datasets spanning Cine-MRI, perfusion CT, and longitudinal MRI, CRONOS outperforms other baselines, while remaining computationally competitive. We will release code and evaluation protocols to enable reproducible, multi-dataset benchmarking of multi-context, continuous-time forecasting.

Published as a conference paper at ICLR 2026
CRONOS: CONTINUOUS TIME RECONSTRUCTION FOR 4D MEDICAL LONGITUDINAL SERIES
Nico Albert Disch 0 Saikat Royl,30, Constantin UIrich 1 Yannick Kirchhoff': :2.3
Maximilian Rokuss 13 Robin Peretzke o David Zimmerer 770 oo Klaus Maier-Hein-.2.44 12.11,8.8
Division of Medical Image Computing, German Cancer Research Center, Heidelberg, Germany 2 HIDSS4Health- Helmholtz Information and Data Science School for Health,
Karlsnuhe/Heiddeleerg, Germany
Faculty of Mathematics and Computer Science, University of Heidelberg, Heidelberg, Germany
4 Pattern Analysis and Learning Group, Department of Radiation Oncology, Heidelberg University Hospital. Heidelberg. Germany
Medical Faculty Heidelberg, University of Heidelberg, Heidelberg, Germany
6 Pattern Analysis Learning Group, Department of Radiation Oncology
Heidelberg University Hospital, Helmholtz Imaging, DKFZ, Heidelberg, Germany Mohamed Bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE
(nico. disch) 8akkz... de
ABSTRACT
Forecasting how 3D medical scans evolve over time is important for disease pro- gression, treatment planning, and developmental assessment. Yet existing models either rely single prior scan, fixed grid times, larget global labels, which limits voxel-level forecasting under irregular sampling. We present CRONOS, unified framework ports both discrete (grid-based) and continuous (real-valued) timestamps in one model, to the hest of our knowledge the first to achieve continuous sequence-to- image forecasting for 3D medical data. CRONOS learns spatio-temporal ve- locity field that transports context volumes toward a larget volume at an arbitrary time, while operating directly in 3D voxel space. Across three public datasets spanning Cine-MRI. perfusion CT, and longitudinal MRI, CRONOS outperforms other baselines, while remaining computationally competitive. We will release code and evaluation protocols to enable reproducible, multi-datase benchmark- ing of multi-context, continuous-time forecasting. Code will be made available under ht sttps: / /g/ttbb.bb//////gg//g///.tt...bt
many-to-one prediction from multiple past scans that sup-
wonginodinanll.oooooooo.nnnnniia 4DMed
INTRODUCTION
Longitudinal medical imaging is central to monitoring disease progression, assessing treatment re- sponse, and modeling anatomical development across time (Suter et al., 2022; Rivail et al., 2019; Bernard et al., 2018). Some modalities are inherently spatio-temporal, such ultrasound (US), cine-MRI, videns, perfusion Computer Tomography (CT). Beyond these, repeated clinical quisitions form temporal sequences that may span over months or years and are used for clinical decision making. In ophthalmology, for instance, longitudinal OCT volumes are central to monitor- ing progression of age-related macular degeneration and predicting treatment response (Rivail et al., 2019). Works such using surgical video streams (Li al., 2024), which also increasingly leveraged diverse tasks, or in (Gomes et al., 2022). where longitudinal US sequences are used, show the overall breadth of spatio-temporal imaging. Beyond individual modalities, there is also a massive and growing amount of video and longitudinal data across clinical contexts (Farhad et al., 2023), including applications such treatment response prediction in oncology (Suter et al., 2022).

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Published as a conference paper at ICLR 2026
lask
Last Contedt image
15 Memory vS Input Range
Ararogi 55W
100
Contrunte Docrelo
16
JANKN SOE DHQ
Cenaoi Inpel
Tagge
Time
02:00 range]
(a) Task description.
(b) Memory Efficiency vs. Performance
Task and benchmark comparison (a) Task setup Forecasting target 3D scan from multiple past volumes in two regimes. Discrete: acquisitions lie approximately regular grid, but may contain missing frames (dotted boxes). Continuous: acquisitions occur irregular, real-valued timestamps and are used directly without grid alignment. Many-to-one task (47,) mmrger) + Iurget- (b) Efficiency and performance Left: GPU memory scaling of single forward pass with sequence length T shows CRONOS be substantially more memory-efficient than alternatives. datasets, where CRONOS outperforms baselines and LCI.
Figure 1:
Right: Average SSIM
Despite its importance, spatio- temporal learning in medical imag- ing is centered mostly single time- point (image-to-image) analysis.
Category
Method
C1
C2
C3
C4
BrLP
X
/
Med. Gen
LociDifiCom
X
/
/
X
ImageFlowNNet
X
/
1
Some approaches rely on global la- hels e.g. Yoon et al. (2024), while many reduce to image-to-image pre- diction with single context scan (Zhang al., 2025a)). Others in- troduce task specifc prior or remain tied to one disease (e.g. Puglisi et al. (2025). In particular, Alzheimer's Disease (AD) has attracted dis- proportionate share of longitudinal imaging research (Petersen et al., 2010; Marti-Juan et al., 2020; Chen al., 2025), whereas other domains remain comparatively underexplored.
Vid. Gen
MCVD
V
/
X
x
SimVP
ViVIT
x
STL
ConvLSTM
/
NODE+LSTM
Med. STL
CRONOS (ours)
Table I: Technical comparison of spatio-temporal pre- diction methods. Columns denote Challenges (C#):: C1: Multiple Inputs. C2: High Fidelity, C3: 3D Imaging. C4: Continuous- Time Modeling. Our proposed CRONOS sat- isfies all four criteria, whereas existing medical and natural imaging baselines lack one more. STL stands for spatio- temporal learning.
CRONOS addresses these challenges by introducing a unified spatio- temporal flow framework for medical scquence-to-image to-image prediction that:
Supports both discrete and continuous timestamps, leveraging multiple past scans
jointly on 3D medical imaging data.
Avoids disease-specific assumptions, enabling application to any medical longitudinal task.
Consistently outperforms prior approaches, including standard sequence models and the Last Context Image (LCI) baseline. which is surprisingly simple and competitive heuristic (NRMSE, PSNR, and SSIM), due to slowly changing medical images.
'Code will be released github. com/ anonymous.
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RELATED WORK
Medical Imaging Prior work in longitudinal medical imaging focuses heavily one-to-one, one-to-many video prediction. While approaches like diffusion models (Litrico al., 2024; Zhu et al., 2024b; Puglisi et al., 2025) and Neural ODEs (Lachinov et al., 2022; Liu ct al., 2025) have been applied to medical imaging, these image-to-inage, and thus cannol canonically capture multi- input longitudinal evolution. For example, Bai Hong (2024) propose continuous-time model, but they predict sequences from single images. contrast, works that jointly leverage multiple observations show improved prediction accuracy (Fang et al., 2021). The single-context nature makes these aforementioned works not sufficient for our setting. There are also interpolation- based methods (Zhu al., 2024a) which predict intermediate frames between acquisitions, but this restricts
use to filling missing intervals rather than forecasting. Overall, existing medical approaches are all technically restricted; be it only single-image input, disease specific priors, limited to 2D, or not being able to forecast to arbitrary times shown in 1.
Description
Data
Legend
flow step time
Flow Trajectory
A Xg 90 leua Fransw
Enrget
[: real time
Xu: Source Distribution
X
Targer
Flow Network
X₁: Target Disteibution
CRONOS: Discrete
CRONOS: Continuous
Inpul and Output
va(2, 7)
Contrune scaoet burra
Val Jr
macing
Xg
Flow Step
X1
X
Observed times
X2
In Sazges
Plew
Roal Time
Xx 13,
Flow Stipe
Stops
Frarget
Figure 2: CRONOS method overview: Left: Discrete CRONOS treats time implicitly, interpo- lating between context frames and fixed target along normalized flow step E [0, 1]. Right: Continuous CRONOS explicitly conditions on real-valued timestamps t, allowing each context to transport toward the target via its own interpolation f,. This enables predictions at arbitrary target times while preserving the true temporal geometry.
By contrast, our work focuses on continuous-time modeling across full spatio-temporal sequences without restricting to specific modalities or diseases.
Natural Imaging and Video Prediction Spatio-temporal modeling has been extensively stud- ied video prediction. Early approaches such as ConvLSTM (SHI et al.. 2015) introduced re- current seneence-t-sequeeee
architectures and remain widely used. Subsequent methods such as SP (Gao et al., 2022) replaced recurrence with purely convolutional designs. Transformer based models like VIVIT (Arnab al., 2021) extended attention mechanisms the video domain and have become a backbone many imaging domains. More recent efforts have explored generative mod- eling. including video diffusion (Voleti et al., 2022: Ye & Bilodeau, 2023; Yan et al., 2021), and continuous-time formulations such as Neural ODEs (Chen et al., 2019), extended to videos in (Park al., 2021). While these approaches are powerful, they have primarily been developed for dense
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natural video sequences with large-scale training data. Accordingly, they transfer poorly to 3D medical images with small datasets and sparse sequences, thus motivating our work.
Flow Matching Flow Matching (FM) has recently emerged as a generative modeling paradigm (Lipman al., 2023; 2024), and has been adapted to irregular time series, c.g. in (Zhang al., 2025b), though only for low-dimensional data rather than full image sequences. Our extension therefore is: while classical FM learn single flow from (most often) raw noise Xo ~ to samples Xi along steps 7 E [0, 1), we re-cast
Xo [41.....A4)) Lr]:
X1 Iurga == [Augett ..... Aurgal]
(1)
interpreting p as the context sequence, and g as a broadcast stack Turget ( defined the stack as Tuager. to make dimension explicit). This temporal broadcasting turns FM into sequence-to-image transport: shared velocity field by simultaneously moves all T context volumes toward the target, effectively T per-frame transports under shared parameters. We refer to this framework Contin- uous RecOnstructioNs for medical 1Ongitudinal Series (CRONOS).
3 METHODS
Algorithm 1 CRONOS Continuous: Training and Inference
Require: Patients P and initial network ey
1: while training
2:
Sample [[I, ] [f1,..., ,,,,,,T,,,n, Aurgea)) 13 P(x))
b. pick random patient random flow step repeat target T times b interpolate timestamps linear interpolation velocity loss
3: Sample ~ (0,
4:
Itarget f- Itrgets- ., Jearges]
5:
T [1
X + [1 7) [1, I...... Lnl + baargst
6:
+ Itarget + (
7:
Le (T, (T, (Iraret T)112
8:
Update 0 AdamW((VoL)
9:
return Ue
10:
inference then
11:
Initialize Xa I
12:
TN = (1 T) ... La] 7 larget
Define integration grid too 0, IN... 1] with N steps
13:
XO.N + ODEInt(ve, Xo, .T....., Ti²))
numerical integration
15:
return Xx
3.1
PROBLEM SETUP
((n) Largett r/m) }" I==1 denote dataset of patient sequences. Each (patient) sequence consists of T context volumes I = (II....,rr) with I, S H x ated timestamps (!1....,tr) .r) C Rt. We consider two regimes. Discrete: Acquisitions lie uniform time grid; some frames may be missing, yielding sparse sequences (e.g., natural video, cine-MRI perfusion CT), Continuous: Acquisitions occur at irregular, real-valued times that do not casily align to any grid (typical in longitudinal clinical scans), For continuous series, forcing a frame grid cither explodes sequence length with empty slots loses temporal precision. For instance,
Let = (0=(((()) ((( d
P
a set
RilxDxW (for shorthand W), acquired associ-
Figure 3: Qualitative comparison on the ACDC dataset. Ground truth (GT), Last Context Image (L.CT), our method (CRONOS), and VP. Up- per row: prediction, lower row: residuals.
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daily-resolution for timepoints over several years would yield T in the thousands, yet in practice only a handful of scans are ever acquired. In both discrete and continuous series, T small relative to natural video.
Target Task. Given the set of context images and ((,, 4)]T- well as target time target. aim to learn
S(1,, 44 harget) >> eagget
(2)
The discrete setting uses a fixed grid (with optional zero-tensors for missing context volumes); the continuous setting uses the observed context only, without padding.
3.2 FLOW MATCHING (FM)
Flow Matching Lipman et al. (2023) learns ordinary differential equation (ODE), linking the equal dimensional distributions p and q via
x + L. (x.)
(x) (x),
(3)
d7
with Xo ~p, X1 q. A convenient coupling obtained by sampling X, as X, = (1 - -) + TXi + a(T),,
(4)
where e ~ (0, I) denotes random gaussian noise (T) its intensity, which is sampled around the straight path. The corresponding ground-truth velocity along this path is therefore constant:
(X+)
X, X1 Xo-
dr
Consequently, to approximate the ground truth velacity, we train a neural network vo(X,,7) R using:
LCFM X,.r |ea(X,, u, (X+) Using to, then infer using equation 3 via approximate ODE solver.
(6)
3.3 CONTINUOUS DISCRETE RECONSTRUCTIONS MEDICAL (CRONOS)
SERIES
We introduce CRONOS, a spatio-temporal flow model that learns continuous trajectories from lon- gitudinal scans. It comes in two complementary variants: discrete and continuous.
Temporal broadcasting for sequence-to-image flows To enable flow between sequence of con- text images and single target, we define Xo the stack of context images (with variant- specific handling for continuous discrete), and X1 g the target image broadcast the same shape
X1 = [
(7)
This broadcasting ensures that Xo and X1 share the same dimensionality, allowing us to define a valid flow between them.
Diserete CRONOS.
On a regular grid with missing scans, we first embed each sequence onto the grid of a resolution using binning operator Egrid which assigns each I; to the closes grid index matching I (proper defimition in A.I.I). Missing slots then handled by last-observed carry- forward operator FLOCP, which fills empty positions with the most recent available sean. In short, we define
Xo = (FLOGP
egrid ((((,, 4012.) 14
[x)
EiIl
ban grid
This pre-procee processing ensures Xg is well-defined on a uniform grid. Furthermore, LOCF handles spatial missingness: missing frames are zero-initialized and replaced by the most recent observation (Appendix A.1.2). This setup stabilizes optimization and preserves grid order while enabling many- to-one sequence transport within FM. Finally, we train on the linear interpolation X, (1-7).x, TX1 using equation 6, where temporal order is captured implicitty by the flow step 7 and the frame index. Additionally, we set 0 during training and inference, ablations on nonzero noise levels reported in Table 7.
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Continuous CRONOS Our continuous modeling stralegy extends on the discrete case by con- ditioning on real-valued timestamps while evolving along a scalar flow parameter T E [0, 1]. We construct spatio-temporal tensors (using mild abuse of notation): Time enters the network only as conditioning real timestamps. We interpolate the conditioning timestamps along the interpolated time vector T,. Xo is then defined as equation equation 7, without embedding to the grid, nor performing LOCF as in discrete CRONOS. We define the shifted time vector as
T- = (1 - 7) fitt + T target-
The formulation in equation lets flow step carry real temporal information, without adding extra complexity. The conditional trajectory then
X = Xo+ [ ud(x, Tr) dr.
(10)
where vo is the predicted velocity field and is the flow step (usually called time, we avoid it due to avoiding confusion). Prediction is then done via approximale solution of equation 3, solver details found in C.I. This formulation lets CRONOS model continuous image evolution grounded in actual scan times, supporting interpolation or forecasting without regular sampling artificial frame filling. It avoids zero-padding. leading to reduced computational burden compared the discrete variant. Both variants use the same 3D U-Net backbone, further details are provided Appendix C.3, and the training/inference procedure appears in Algorithm 1.
Time Encoding. Flow steps and continuous times mapped to Fourier embeddings ing (Tancik al., 2020), which were used e.g. (Rombach al., 2022): 7(t) (sin(27ffef), cos fi)) using frequencies fi- To preserve dimensional consistency across veriable-length input sequences for the continuous setting, we compute the time embedding as
Enc(t)
1 T
Σ ((.).
(11)
This embedding is then added to each residual layer via FILM. The loss then calculated via equation 6, and inference via equation 10.
4 DATA AND EXPERIMENTAL DESIGN
4.1 DATASETS
ACDC (Bernard al., 2018) a cardiac MRT dataset cap- turing different heart phases. The context tensor is reshaped to [T. H, D. D. = [11, 32, 128, 128), and the target is sin- spatial size. We split ACDC into 80
ODASS
gle image with the training, 20 validation
50 test images. This dataset served for method development: ablations were conducted on the val- idation split.
ISLES (Riedel al., 2024) consists of perfusion CT image time series from stroke patients. From the normalized series, we sample consecutive points, take the last as the target, and randomly mask the remaining context frames. The resulting context tensor has shape [T', H, D. use a split of training, 23 validation and test images. For both the ACDC and dataset, we randomly mask out time points (see Appendix C.2). Lumiere (Suter et al., 2022) is longitudinal glioma MRI dataset with 3D scans. Images are reshaped to [T, H. D, W] [7, 96, 96, 64]. Because some patients have few acquisitions, we prepend zeros to standardize pre-processing across cases. The split is 48 training, 12 validation and 14 test images.
[7. 16, 128, 128). We
Figure 4: Qualitative compari- son on the LUMIERE dataset. Ground truth (GT), Last Con- text Image (LCI). our method (CRONOS), and SP baseline. Lumiere is particularly challeng- ing due the very small dataset. highlighting the benefit of explicit continuous-timg conditioning extreme data scarcity.
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EXPERIMENTAL SETTINGS
Reproducibility details can be found in Section C.
Discrete Setting: As mentioned in the data section, input data has dimension T. while some frames may be missing. We apply both variants of CRONOS, noting that the continuous version can also operate in this regime with smaller context window, since missing images do need be explicitly represented. The lower context window also leads to a lower computational demand. Therefore, the underlying tensors remain uniform, with some time points masked. For validation and testing we ensure that the missingness pattern is fixed across epochs, as otherwise the choice of best checkpoint would be ill- ull-posed (further details in Appendix C.2).
Continuous Setting: As additional ablation and experiment, simulate continuous setup ACDC highlight the gains from explicit timestamp conditioning. While public dataset provides plenty of continuous acquisition protocols, this sub-sampled variant shows that CRONOS benefits from real-valued time even heyond irregular masking. Specific details of how we subsampled ACDC can be found in C.I. Importantly, both the discrete and continuous formulations remain applicable discrete grids.
Table 2: Discrete Time: Quantitative Evaluation Many-to-One Sequences: Reported values mean (standard deviation) over three runs. Metries include normalized root M MSE NRMSE, SE, structural similarity index (SSIM (%]) and peak signal-to-noise-rate PSN *ViVIT OOM on a 40 GB GPU, despite having a smaller batch size and the lowest possible feature size. Standard deviation of LCI omitted for visual clarity. Blue row: only method to beat LCI and our proposed CRONOS. Computational requirements ACDC in
Dataset
Model
NRMSE [10-
SSIM [%]] f
PSNR [dB]
ACDC
LCI
4.48
92.79
28.918
COnVLSTM
11.20 0.48
50.44 1.53
19.123 0.312
SimVP
9.27 # 0:29
49.08 + 4.01
20,715
0.267
NODE LSTM
11.59 + 0.18
36.41 10.412200 2.94
18.946
0.186
ViVIT
13.90 2.66
17.06 8.60
17.252 1.738
CRONOS discrete
3.97 1.23
94.51 0.79
30.510
1.560
CRONOS cont.
3.74
94.34 0.45
29.750 + 0.528
ISLES
LCI
5.25
96.29
29.002
ConVLSTM
19.31 + 0.18
39.92 1 0.66
17.644 1 0.014
SimVP
13.06 + 0.19
48.82 + 1.60
20.799 # 0.1
VIVIT
16.54 0.30
36.76 1.49
18.671 0.134
NODE LSTM
15.10
40.55
19.481 + 0.515
CRONOS discrete
4.50 + 0.76
97.33 0.93
30.542 # 1.540
CRONOS cont.
4.38 + 0.48
97.31 + 0.38
30.809 # 1.099
Lumiere
LCI
8.38
88.35
21.631
COMVLSTM
34.79 + 0.67
9.21 2 2,81
9,217 # 0.171
SP
71.03 = 0.89
-1.92 0.51
2.989 + 0.109
ViViT*
OOM
0OM
0OM 17.742 + 0.659
NODE+LSTM
13.07 + 1.03
48.66 2 2.26
CRONOS discrete
7.92 + 0.92
91.43 + 1.84
22.427 # 0.969
CRONOS cont.
7.55 + 0.86
89.32 1.83
22.551 # 0.979
Baselines We compare CRONOS against established peatioltemporal learning methods. As clin- ically motivated heuristic, the Last Context Image baseline (LCI) simply reuses the last available image and serves as a lower bound. Among sequence models, we include ConVLSTM (SHI et al., 2015). Sim VP (Gao et al., 2022), and VIVIT (Arnab et al.. 2021) as representative recurrent, convo- lutional, and transformer backbones. For continuous-time sequence modeling, further evaluate an ODE-LSTM (Lechner & Hasani, 2020) baseline. For the flow matching library we use Tong et al. (2024b;a); Tong (2025). Together, these methods provide a spectrum of spatio-temport ar- chitectures against which we benchmark CRONOS. Computational requirements are described in detail in the appendix.
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Continuous vs, Discrete. We report results in two regimes: an discrete setting, which allows direct comparison to existing spatio-temporal baselines, and a continuus setting on ACDC, designed as an ablation to test the benefit of explicit timestamp conditioning.
5 RESULTS AND DISCUSSION
5.1 TOWARDS UNIFIED BENCHMARKING FOR MEDICAL 3D SEQUENCE- -O-NNAGE FORECASTING
are among the first to propose an experimental setup for gqquence-to-imae task, evaluating CRONOS under two complementary regimes. The first uses discrete input sequences, where some context images are missing but acquisitions lie on regular grid. This setting enables comparison against established spatio-temporal baselines. The second uses ACDC with resampled acquisitions mimic continuous input, allowing us assess the benefit explicit timestamp conditioning. For completeness. we include an image-to-image (not sequence-te to to-image) diffusion baseline on ACDC (dctails in B.5) This required a two-stage training setup, first pretraining an autoencoder and then training the diffusion module for 1000 denoising steps, which already made the approach far computationally demanding than all other baselines. Iterative denoising leads order-of- magnitude longer inference time for a single image-to-image step and several orders of magnitude higher training cost, while not surpassing the simple LCI heuristic.
5.2 CRONOS IS STATE-OF-THE-ARE FOR SPATIO-TEMPORAL 3D MEDICAL IMAGE FORECASTING
Table 2 reports the quantitative results across all three datasets. We observe that both variants of CRONOS substan- tially outperform the competing spatio- temporal baselines, also note that individually, CRONOS is better than LCI on each individual val- idation rum. On LUMIERE, which is characterized by very sparse and hetero- geneous tumor trajectories, it is surpris- ing that CRONOS is even able outper- form LCI. These results demonstrate that CRONOS is effective across different tem- poral regimes: the discrete formulation al- ready yields strong performance, while the continuous formulation provides further gains when timestamps are informative. CRONOS runs within the same computational budget during in- ference (see Figure 1b) and in similar orders of magnitude (VRAM and wall-clock time) during training as natural imaging baselines (see 8). Further ablations are provided in A, confirming that CRONOS is stable across variations in feature size, training noise, and inlegration settings. While small differences appear, they are not substantial, indicating that our network highly robust to hyperparameter choices.
Method
SSIM
PSNR 1
NRMSE
LCI
93.27
29.77
0.0349
well as LCI. We
NODE+LSTV
57.50
22.87
0.0728
CRONOS discr.
93.27
29.77
0.0348
CRONOS cont.
93.86
30.09
0.0330
Table 3: Continuous ACDC, where discrete CRONOS lacks explicit timestamp conditioning, and therefore fails oulperform LCI. Additional experiments in and in Table 9
CRONOS ENABLES EFFICIENT FLOW- BASED CONTINUOUS MEDICAL MODELING
Table demonstrates that incorporating explicit time embeddings improves forecasting quality when scans occur at irregular intervals. This shows that the continuous formulation of CRONOS is not only feasible but also beneficial in realistic clinical settings, where images are often irregularly sampled. In fact, if fully remove the timestamp information entirely, performance differences increase significantly, and the continuous variant clearly outperforms the discrete one 9. Together, these results highlight that modeling real-valued timestamps can provide a measurable advantage over treating sequences as grid-aligned. However, in Table 2, see that using the discrete variant
"On our setup, naive auto-regressive mmage-to-image latent-diftusion pipeline applicd across context times per subject requires ~5 6 hours per validation step; Appendix A for details.
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Imsge
GT Flow
Ing. Flow Prod
Figure 5: Network Flows: Top: input images at the first five timestamps. Middle: tround-trutth
voxel-wise differences (T / Bottom: predicted velocity fields vo (Xo, 0), overlaid on the cor- responding inputs. The highlighted regions coincide with the areas of the largest temporal changes (primarily the ventricular cavities and myocardial boundaries).
remains highly competitive. Although any irregular series in principle be quantized grid via Egrid doing so without loss requires increasingly fine grids. This becomes computationally inefficient, whereas the continuous variant scales with the number of context images and not with the grid range K' A (see equation 12). This is reflected in Table and Figure 1b, where continuous CRONOS is both more memory-efficient and faster train than the discrete formulation. It also highlights broader limitation of the field: scarcity of diverse spatio-temporal datasets which real timing information is critical.
5.4 CRONOS PRODUCES SHARPER RECONSTRUCTIONS WIT LOWER RESIDUALS
Figures 3, 6 and highlight qualitative comparisons, as well as datasel exam- ples. The LCT baseline often appears visually close to the target, largely be- cause many longitudinal scans exhibit only subtle changes. However, e.g. SimVP tends to introduce artifacts and blur anatomical details. In contrast, CRONOS yields s reconstructions and consistently lower residuals com- pared to LCI, highlighting its ability to capture fine-grained temporal progres- sion.
Gl
LCI
CHONC' (ours)
Smm
Zoomed-in qualitative comparison the ISLES dataset. Ground truth (GT), Last Context Im- age (LCI), our method (CRONOS), and Sim VP bascline. Shown here for visibility is zoomed in patch of the qual- itative results of the ISLES dataset.
Figure 6:
5.5 FUTURE WORK: UNLOCKING GENERAL SPATIO-TENT TEMPORAL MEDICAL FORECASTING
While voxel-wise fidelity metrics such as NRMSE, PSNR, and SSIM remain the community standard, they do not fully capture clinically relevant trajec- tory modeling. As highlighted in recent efforts image analysis validation Maier-Hein al. (2024), such metries may not always align with actual domain interest. Developing metrics for spatio- tempora forecasting is therefore an important future direction. In parallel, the scarcity of longitudinal and spatio-temporal datascts (beyond the ones we used in this study), poses a broader challenge for robust evaluation. Encouragingly, results on LUMIERE suggest that progress is
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possible even under severe data limitations, and we hope to motivate further work on curating larger and more diverse publicly available cohorts. Finally, the absence of large-scale foundation models for medical imaging, particularly in the spatio-temporal domain, remains major bottleneck. We view our work keystone contribution; establishing unified flow-based framework for continu- ous spatio-tenn ppapool medical volumetric forecasting that can both benefit from, and motivate, future developments in medical imaging.
6 CONCLUSION
In this work, presented CRONOS (Continuous RecOnstructioNs for medical 1Ongitudinal Se- ries), a unified spatio-temporal framework that forecasts 3D medical volumes arbitrary target times by combining multiple context scans with explicit real-valued time conditioning. Unlike single-image time-agnostic methods, CRONOS handles both grid-aligned and continuous times- tamps within one architecture, and makes disease-specific assumptions. It is among the first meth- ods to demonstrate continuous siquence-to-image forecasting for 4D medical data. Across three publicly available datasets (Cine-MRI, perfusion CT. longitudinal MRI), it outperforms baselines- including the strong Last Context Image (LCI)-and remains robust under hyperparameter changes while remaining computationally competitive. By resolving the aforementioned limitations, method enables clinically specific studies and advances patient-level forecasting for personalized precision medicine.
BROADER IMPACT
Longitudinal modeling of medical images has the potential improve patient by enabling ear- detection of disease progression, monitoring of treatment response, and improved personaliza- tion of therapy. By explicitly modeling continuous temporal evolution, our approach could support clinicians in making more informed decisions. However, there are also risks: mispredictions may lead to incorrect clinical conclusions if models are deployed without careful validation and without human the loop. Biases in training data (e.g., underrepresentation of certain populations imag- ing modalities) may propagate to predictions, raising concerns about fairness and generalizability, which is a common problem in medical imaging. We emphasize that our method is a research con- tribution intended to advance especially technical methodology. Clinical deployment would require extensive validation, regulatory approval, and integration into existing workflows. We believe that by releasing code benchmarks, this work will support the community in building transparent, reproducible, and safe spatio-temporal models for healthcare. But by proposing this method, we hope to support general-purpent foundation for medical spatio-temporal and longitudinal model- ing, which could massively propel this area forward.
ACKNOWLEDGMENT
The present contribution is supported by the Helmholtz. Association under the joint research school "HIDSS4Hcalth Helmholtz Information and Data Science School for Hcalth. N.A.D. and Y.K. were funded by HIDSS4Health, D.Z. was funded by HELMHOLTZ IMAGING, a platform of the Helmholtz Information & Data Science Incubator, C.U. was funded by the Helmholuz Foundation Model Initiative (HFMI) through the pilot project THRP (The Human Radiome Project). M.R. was funded via the Phd Program DKFZ, R.P. was funded by the Deutsche Forschungsgrmeinsshaff (DFG, German Research Foundation) 536508040.
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REFERENCES
Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučié, and Cordelia Schmid. ViVIT: A Video Vision Transformer. pp. 6836-6846, 2021. URL httptss://ppeacceeeeeee /opeaacesss.
thscvf.com/conttt http://....ppp......eeeeeeeeteea
Transformer_ 2021
Hao Bai and Yi Hong- NODER: Image Sequence Regressionn Regresion Based Based on Neural Ordinary Differential Equations, July 2024. URL http:://aarti...rgg////////0//// [es].
arXiv:2407.3241
Olivier Bernard, Alain Lalande, Clement Zotti, Frederick Cervenansky, Xin Yang, Pheng-Ann Heng, Trem Cetin, Karim Lekadir, Oscar Camara, Miguel Angel Gonzalez Ballester, Gerard San- roma, Sandy Napel, Steffen Petersen, Georgios Tziritas, Elias Grimias, Mahendra Khened, Vargh- Alex Kollerathu, Ganapathy Krishnamurthi, Marc-Michel Rohé, Xavier Pennec, Maxime Sermesant, Fabian Isensee, Paul Jäger, Klaus H. Maier-Hein, Peter M. Full, Ivo Wolf, Sandy Engelhardi, Christian Baumgartner, Lisa M. Koch, Jelmer M. Wolterink, Ivana ligum, Yeong- gul Jang, Yoonmi Hong, Jay Patravali, Shubham Jain, Olivier Humbert, and Pierre-Mare Jodoin. Deep Learning Techniques for Automatic MRI Cardiac Multi-Structures Segmentation and Di- agnosis: the Problem Solved? IEEE Transactions
Medical Imaging, 37(1 1751122554 doi: 10.1 11L1100//M.22018885777777 ieee wwt.//eeereeeeeeeeeeeeeeeeeeeeee dttpm/nt////neeeeee /eecument/8304453/ /8360433/
November 2018. ISSN 0278-0062, 1558-254X.
URL
Durong Chen, Meiling Zhang, Hongjuan Han, Yalu Wen, and Hongmei Yu. Reflections on dy- namic prediction of Alzheimer's discase: advancements in modeling longitudinal outcomes and time-to-event data. BMC Medical Research Methodology, 25(1):175, July 2025. ISSN 1471-2288. doi: 00.118661228744-255-266188-- s12874-025- 02688-x
URL https://dol. http///....g/..11//.....
Ricky T. Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud. Neural Ordinary Differential Equations, December 2019. URL http:/ /arp:v//aaavv...//a org/ aww//806... 07366. arXiv:1806.07366 [cs].
Cong Fang, Song Bai. Qianlan Chen, Yu Zhou, Liming Xia. Lixin Qin. Shi Gong, Xudong Xie, Chunhua Zhou, Dandan Tu, Changzheng Zhang, Xiaowu Liu, Weiwei Chen, Xiang Bai, and Philip H. S. Torr. Deep learning for predicting COVID-19 malignant progression. Med- ical Image Analysis, 72:102096, August 2021. ISSN 1361-8415. doi: 10.1016/j.mddia.
2021..02096. URL https:/ http:://wwwwww.. wwwp::/.cienneeiieee..... www.///iiene//artcceee.... 51361841521001-0
Moomal Farhad, Mohammad Mehedy Masud, Azam Beg, Amir Ahmad, Luai Ahmed. Review of Medical Diagnostic Video Amalysis Using Deep Learning Techniques. Applied Sciences, 13(552,, January 2023. ISSN 2076-3417. doi: 10.3390/app13116582 URL
https: /www. mdpi. mtddi.ccm/2000 ital Publishing Institute.
Publisher: Multidisciplinary Dig-
Zhangyang Gao, Cheng Tan, Lirong Wu, and Stan Z. Li. SimVP: Simpler Yet Better Video Prediction, pp. 3170-3180, 2022. URL https: httpss///ppacccsssseeeee thecvf.com. conoet//t/////////o/o//o/o CVPR2022 http2/httm///// /Gao Saraaa_Ssmvm__SS Siine__simpler__ee_eeeeeeeeeeeee Sttt widee___eeeee_eeeiiitioooo CVPR_ SUPP__022__ppeer html..
Ryan G. Gomes, Bellington Vwalika, Chace Lee, Angelica Willis, Marcin Sieniek, Joan T. Price, Christina Chen, Margaret P. Kasaro, James A. Taylor, Elizabeth M. Stringer. Scott Mayer McK- inney, Ntazana Sindano, George E. Dahl, William Goodnight III, Justin Gilmer, Benjamin H. Chi. Charles Lau, Terry Spitz. Saensuksopa. Kris Liu, Jonny Wong. Rory Pilgrim, Akib Uddin, Greg Corrado. Lily Peng. Katherine Chou, Daniel Tse, Jeffrey S. A. Stringer, and Shravya Shetty. Al system for fetal ultrasound in low-rcsource settings, March 2022. URL http://arxiv.ort abs/2203- 20139. 1019. arXiv:2203. 101399 [cs].
Dmitrii Lachinov, Arunava Chakravarty, Christoph Grechenig, Ursula Schmidt-Erfurth, Hrvoje Bogunovic. Learning Tentool Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data, November 2022. URL. http:://axxiii http:///xxvvo.ogabbbbee org//bs//21111 04234, Akiv:2211.042:: [cs].
11

---

Published as a conference paper at ICLR 2026
Mathias Lechner and Ramin M. Hasami. Learning Long-Term Dependencies in org/paper/ paper/
Time Series. ArXiv, June 2020. URL http://:////ww..eeettttccccoooo
Yunlong Li, Zijian Zhao, Renbo Li, and Feng Li. Deep learning for surgical workflow anal- ysis: survey of progresses, limitations, and trends. Artificial Intelligence Review, 57(11): 291, September 2024. ISSN 1573-7462. doi: 10. 1010007/104422-22-100000 10929-6. URL https:
//doi. 0tt/10.rg11... 600462 -
Yaron Lipman, Ricky T. Q. Chen, Heli Ben- HamuH Maximilian Nickel, and Matt Lc. Flow Matching for Generative Modeling, February 2023. URL http:://axxii org/ arXiv:2210.22747 [es].
02747.
Yaron Lipman, Marton Havasi, Peter Holderrieth, Neta Shaul, Mall Le, Brian Karrer, Ricky Q. Chen, David Lopez-Paz, Heli Ben-Hamu, and Itai Gat. Flow Matching Guide and Code, Decem- ber 2024. URL http::tt///... http::///aaxvv.vaeae
/2222. 64.64. arXiv:2412.0622 [cs].
Mattia Litrico, Francesco Guarnera, Mario Valerio Giuffrida, Daniele Ravi, and Sebastiano Bat- tiato. TADM: Temporrally-Aaare Diffusion Model for Neurolegenerattie Progression on Brain MRI. In Marius George Linguraru, Qi Dou, Aasa Feragen, Stamatia Giannarou, Ben Glocker, Karim Lekadir, and Julia A. Schnabel (eds.), Medical Image Computing and Computer Assisted Intervention MICCAI MICCAI 2024, volume 15002, pp. 444-453. Springer Nature Switzerland, Cham, doi: 10. 1007/998---000111111 3-17788----11---666 -70699777777777-- 42. URL https: /ts:://1/ //ink.......///////mm sppringer.... wwm/ccmcccc/ooo 1007 / 031 72061-7722292222 42.
2024. ISBN 978-9-001-77208--0 978-3-031-72066977
Series Title:
Lecture Notes in Computer Science.
Chen Liu, Ke Xu, Liangbo L. Shen, Guillaume Huguet, Zilong Wang, Alexander Tong, Danilo Bz- dok. Jay Stewart, Jay C. Wang, Lucian V. Del Priore, and Smita Krishnaswamy. ImageFlowNet: Forecasting Multiscale Image-Level Trajectories of Disease Progression with Iregularly-Sampp Longitudinal Medical Images, April 2025. URL http: //tpxv/./vvv///////////.//a.aa wwtp/oo///////o//ooooo 14794. arXiv:2406.14:5 14794 [eess].
Lena Maier-Hein, Annika Reinke, Patrick Godau, Minu D. Tizabi, Florian Buettner, Evangelia Christodoulou, Ben Glocker, Fabian Isensee, Jens Kleesiek, Michal Kozubek, Mauricio Reyes, Michael A. Riegler, Manuel Wiesenfarth, Emre Kavur, Carole H. Sudre, Michael Baumgartner. Matthias Eisenmann, Doreen Hockmann-Nörzel. Tim Rädsch, Laura Acion, Michela Antonelli, Tal Arbel, Spyridon Bakas, Arriel Benis, Matthew B. Blaschko, M. Jorge Cardoso, Veronika Cheplygina, Beth A. Cimini, Gary S. Collins, Keyvan Farahani, Luciana Ferrer, Adrian Gal- dran, Bram Ginneken, Robert Haase, Daniel A. Hashimoto, Michael M. Hoffman, Merel Huisman, Pierre Jannin, Charles E. Kahn, Dagmar Kainmueller, Bernhard Kainz, Alexandros Karargyris, Alan Karthikesalingam, Florian Kofler, Annette Kopp-Schneider, Anna Kreshuk, Tahsin Kurc, Bennett A. Landman, Geert Litjens, Amin Madani, Klaus Maier-Hein, Anne L. Martel, Peter Matison, Erik Meijering. Bjoern Menze, Karel G. M. Moons, Henning Müller, Brennan Nichyporuk, Felix Nickel, Jens Petersen, Nasir Rajpoot, Nicola Rieke, Julio Saez- Rodriguez, Clara Sánchez, Shravya Shetty, Maarten van Smeden, Ronald M. Summers, Ab- del A. Taha, Aleksei Tiulpin, Sotirios A. Tsaftaris, Ben Van Calster, Gaël Varoquaux, and Paul F. Jäger. Metrics reloaded: recommendations for image analysis validation. Nature Methody, 21(2):195-112 February 2024. ISSN 1548- doi: 10.10081441192--2200225555 20tp////222222222221111
URL Publisher: Nature
https://wwwnatuureecc www.nntuue....m... www. Publishing Group.
Gerard Marti-Juan, Gerard Sanroma-Guell, and Gemma Piella. A survey machine and statis- tical learning for longitudinal analysis of neuroimaging data in Alzheimer's disease. Computer Methods and Programs in Biomedicine, 109:10 June 2020. ISSN 0169-2607. doi: 10.1016/ j.cmpb22000.1 105348. URL https:/ htapp::///wwww//////// www. wcwencedirect...... com/ wttp:/etttcccccceeeeeeeeeeeeeeee wttm///ciene//articllel. pii/$01692600 09200069967775 93116165.
Sunghyun Park. Kangyeol Kim, Junsoo Lee, Jaegul Choo, Joonseok Lee, Sookyung Kim, and Ed- ward Choi. Vid-ODE: Continuous- Time Video Generation with Neural Ordinary Differential Equation, March 2021. URL http: httptt:://axxvv.orogg/o orgg 081088188 88. arXiv:2010.00 [cs].
12

---

Published as a conference paper at ICLR 2026
C. Petersen, P S. Aisen, I. A. Becketl, M C. Donohue, A C. Gamst, Harvey, C. R. Jack, W J. Jagust, I. M. Shaw, A W. Toga, J Q. Trojanowski, and M W. Weiner. Alzheimer's Disease Neuroimaging Initiative (ADNI). Neurology, 74(3)2001-29,, January 2010. ISSN 0028-3878. doi: 1111///W0.00003331111111 Aaticles/EMC2BB 00C360906..........
URL htsps: /www. ncbi nlm nih. www.inih......oooooo gwv/pmc/////oooooooooo//////..
Lemuel Puglisi, Daniel C. Alexander, and Daniele Ravi, Brain Latent Progression: delividual-bassee Spatiotemporal Disease Progression 3D Brain MRTs via Latent Diffusion, Fehruary 2025. URL [cs].
http://att //axxi///viii wwg/ 2502. 00.60. arXiv:2502.088.
Evamaria O. Riedel, Ezequiel de la Rosa, The Anh Baran, Moritz Hernandez Petzsche. Hakim Baazaoui, Kaiyuan Yang. David Robben, Joaquin Oscar Seia, Roland Wiest, Mauricio Reyes, Ruisheng Su, Claus Zimmer, Tobias Boeckh- Beecch--eeeens,... Maria Berndt, Bjoern Menze, Benedikt Wiestler, Susanne Wegener, and Jan S. Kirschke. ISLES 2024: The first longitudinal multimodal multi-center real-world dataset in (sub-)acute stroke. 2024. doi: 4.48550/ARXI..2488.... 142.
URL https: : arxiv. org/abs 2400 11142. Publisher: arXiv Version Number: 1.
Antoine Rivail, Unsula Shlmidt-Erfuuthh Wolf-Dieter Vogl, Sebastian M. Waldstein, Sophie Riedl, Christoph Grechenig, Zhichao Wu, and Hrvoje Bogunović. Modeling Discase Progression In Retinal OCTs With Longitudinal Self-Supervised Learning. October 2019. URL http: //arxiv.org//abiii 9100. 09420. arXiv:1910.09420 [eess].
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjom Ommer. High- Resolution Image Synthesis with Latent Diffusion Models. 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10674-10685, June 2022. doi: ieee. oogg/docuentt 9878449/. Conference Name: 2022 IEEE/CVE Conference Computer Vision and Pattern Place: New Orleans, LA, USA Publisher: IEEF.
10.1109CVPR52688.220 20t..02222020.03 URL https:::.
Recogmition (CVPR) ISBN: 978 1654469463
Xingjian SHI. Zhourong Chen, Hao Wang, Dit- Yan Yeung, Wai-kin Wong, and Wang-chun WOO. Convolutional LSTM Network: A Machine Learnnng Approach for Precipitation Now- casting. Advances in Neural Information Processing Systems, volume 28. Curran Asso- ciates, Inc., 2015, URL https: : pro.eediooeeeeeoooooooop neurips cc/ papppe/e01//aaaslll 07563a3fe 3bbe 7 3ww.33155ad0005eeeeoeee
html.
Yannick Suter, Unspeter Knecht, Waldo Valenzuela, Michelle Notter, Ekkehard Hewer, Philippe Schucht, Roland Wiest, and Mauricio Reyes. The LUMIERE dataset: Longitudinal Glioblastoma MRI with expert RANO evaluation. Scientific Data, 91):768, December 2022, ISSN 2052- 4463. doi: 150000/0115---72001888-1-11- URL h==ps: 001597-022-01
www.:naatteee.eeaaeaeeeeaeeeeeee Publisher: Nature Publishing Group.
Matthew Tancik, Pratul P. Srinivasan. B. Mildenhall, Sara Fridovich-Keil, Nithin Ragha- van, Utkarsh Singhal, R. Ramamoorthi, J. Barron, and Ren Ng. Fourier Fea- tures Let Networks Learn High Frequency Functions in Low Dimensional Domains. URL https: /www. semarticscoolar / Preerearen--ii-----rr-rreee--ee Meeer
ArXiv, June 2020.
Patrick Therasse, Susan G. Arbuck, Elizabeth A. Eisenhauer, Jantien Wanders, Richard S. Kaplan, Larry Rubinstein, Jaap Verweij, Martine Van Glabheke, Allan T. Van Ousterom, Michaele C. Christian, and Steve G. Gwyther. New Guidelines Evaluate the Response to Treatment in Solid Tumors. JNCI: Journal of the National Cancer Institute, 92(3):205-216, February 2000. ISSN doi: 10. 1t.1199//nnn//2..... 3.02220 URL ht /tw////aaccmcccc/// mitemmi..om com. com
0027-8874, 1460-2105.
jnci/ wwwttcceee96500000 New. Publisher: Oxford University Press (OUP).
Alexander Tong. TorchCFM, January 2025.
URL https:: http:::///gttuub.com cotp:/ttobb.coo//ttogg/////
conditional Fl wwwe-matchinnn
Alexander Tong, Kilian Fatras, Nikolay Malkin, Guillaume Huguet, Yanlei Zhang, Jarrid Rector- Brooks, Guy Wolf, and Yoshua Bengio. Improving and generalizing flow-based generative models with minibatch optimal transport, March 2024a. URL http: http::////xvvvo..abbsssss.// 2302. 00482. mrXiv:2302.00483 [cs].
13

---

Published as a conference paper at ICLR 2026
Alexander Tong. Nikolay Malkin, Kilian Fatras, Lazar Atanackovie, Yanlei Zhang, Guillaume Huguet, Guy Wolf, and Yoshua Bengio. Simulation-free Schrödinger bridges via score and flow matching, March 2024b. http:// UtL.ttt:://axxx.orrr//////// 201122377702222222 03672. arXiv:2307003672 [es].
Vikram Voleti, Alexia Jolicoeur-Martincau, and Christopher Pal. MCVD: Masked Conditional Vidco Diffusion for Prediction, Generation, and Interpolation. 2022. doi: 10.48550/ARXIV.
2205.09853. URI. https://arxisss org/ abw.abab...2..e../// 2205 09853. Publisher: arXiv Version Number: 4.
Wilson Yan, Yunzhi Zhang. Abbeel. and A. Srinivas. VideoGPT: Video Generation using VQ- VAE and Transformers. ArXiv, April 2021. URL bt::s://p/// /www. semanticschoooooooeooociooccccie org/
ott.://oeooooooooooooooooooooooo www.-eeeeeeennnneeieeieee -iig---- Seeesiinng------- VQ-VAE www--an------ and--an----------- -an---annng----
Xi and Guillaume-Alexante Bilodeau. STDiff: Spatio-temporal Diffusson for Continu- ous Stochastic Video Prediction. 2023. doi: N044550/AXXI22312.6442 URL https:
// //aaxivvoorg abs/ 222 06486. Publisher: arXiv Version Number: 1.
Dan Yoon, Youho Myong, Young Gyun Kim, Yongsik Sim, Minwoo Cho, Byung-Mo Oh, Sungwan Kim. Latent diffusion model-based MRT superresolution enhances mild cognitive impairment prognostication and Alzheimer's s disease classification. Neurolmage. 296:120663, August 2024. ISSN 1053-8119. doi: 10.1066f.euumiimngge222021111110
URL https:
//www. encedirect wttpscc. http:///wwaaaaa.eeooooooeeeettaa
Shaorong Zhang, Tamoghna Chattopadhyay, Sophia I. Thomopoulos, Jose-Luis Ambite, Paul M. Thompson, and Greg Ver Steeg. Diffusion Bridge Models for 3D Medical Image Translation, April 2025a. URL /atp:i:////xv...//////eeeeemm org/ http:/bb//2250/ /204.. 15267. arXiv:2504.1524 [es].
Xi Zhang. Yuan Pu, Yuki Kawamura, Andrew Loza, Yoshua Bengio. Dennis L. Shung, and Alexan- der Tong. Trajectory Flow Matching with Applications to Clinical Time Series Modeling, Febru- ary 2025b. URL http: arxiv wtt. /2410 21154. arXiv:2410.21 [cs].
Zihao Zhu, Tianli Tao, Yitian Tao, Haowen Deng, Xinyi Cai, Gaofeng Wu, Kaidong Wang, Haifeng Tang. Lixuan Zhu, Zhuoyang Gu Dinggang Shen, and Han Zhang. LoCI-DiffCom: Lon- gitudinal Consistency-Inforine
Diffusion Model for 3D Infant Brain Image Completion. In Marius George Linguraru, Qi Dou, Aasa Feragen, Stamatia Giannarou. Ben Glocker, Karim Lekadir, and Julia A. Schnabel (eds.), Medical Image Computing and Computer Assisted In- tervention - MICCAI 2024, volume 15002. pp. 459. Springer Nature Switzerland, Cham, 978-3-031-72069-7. doi: (0.11007/78-3-00 --07778----11-00099 7.24. .224. URL https: ht///innk winiinnkspp.. spr sprinngrr. Titl: Lecture Notes in Computer Scienee.
2024a. ISBN 778-3-031-720668
24. Series
Zihao Zhu, Tianli Tao, Yitian Tao, Haowen Deng, Xinyi Cai, Gaofeng Wu, Kaidong Wang, Haifeng Tang, Lixuan Zhu, Zhuoyang Gu, Dinggang Shen, and Han Zhang. LoCI-DiffCom: Longitudinal -eaistency-IIformmee Diffussin Model for 3D Infant Brain Image Completion. In Marius George Linguraru, Qi Dou, Aasa Feragen, Stamatia Giannarou. Ben Glocker, Karim Lekadir, and Julia A. Schnabel ). Medical Image Computing and Computer Assisted Intervention - MICCA/ 2024, pp. 249-258, Cham, 2024b. Springer Nature Switzerland. ISBN 778-3-031--206697. doi: 10. 3-077788--3-----060000 7.24.
14


Reviews:
[{"review_id": "QMOArHCGGw", "reviewer": "Reviewer_YVaG", "summary": "This paper introduces CRONOS, a flow-based framework for 3D medical image forecasting that learns continuous spatio-temporal dynamics from longitudinal scans.Unlike prior models restricted to single-context or grid-aligned timepoints, CRONOS handles both discrete and continuous timestamps by learning a spatio-temporal velocity field that transports a stack of past volumes toward a future target scan. Technically, the authors reinterpret Flow Matching (FM) (Lipman et al., 2023) as a sequence-to-image transport problem:\n$X_0 = [I_1, …, I_T],\\qquad X_1 = [I_{\\text{target}}, …, I_{\\text{target}}],$ and train a 3D U-Net $v_\\theta(X_\\tau,T_\\tau)$ to approximate voxel-space velocities between context and target. The authors suggested two complementary variants:\n1. Discrete CRONOS: uses grid embedding + last-observation-carry-forward (LOCF) to fill missing frames.\n2. Continuous CRONOS: conditions directly on real timestamps via Fourier embeddings and FiLM.\n\nExperiments on three public 3D datasets—ACDC (cardiac MRI), ISLES (perfusion CT), and LUMIERE (longitudinal glioma MRI)—show consistent improvements over ConvLSTM, SimVP, ViViT, NODE-LSTM, and the simple Last Context Image (LCI) baseline. CRONOS maintains competitive compute cost, yields sharper reconstructions, and performs best when irregular timestamps are available.", "questions": "1. Does the learned velocity field correspond to interpretable motion (can it be visualized or regularized)?\n2. Could CRONOS handle autoregressive multi-step prediction, not just one-step forecasting?\n3. Have you compared with a “zero + mask” imputation instead of LOCF to ensure fairness?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Longitudinal 4D imaging is central to disease progression analysis, yet remains underexplored by the ML community. \n2. Extending FM from noise-to-sample to multi-context-to-target volumetric flows is conceptually creative and unifies discrete and continuous-time modeling within one ODE framework.\n3. The discrete/continuous variants and Fourier-time conditioning offer a simple yet flexible approach adaptable to both regularly and irregularly sampled medical series.", "weaknesses": "1. The “velocity loss” $\\|v_\\theta(X_\\tau,T_\\tau)-(I_{\\text{target}}-I)\\|^2$ treats voxel-intensity differences as flow supervision.\nThis deviates from FM’s probabilistic transport interpretation and lacks theoretical grounding in physical or latent-space dynamics.\n2. ConvLSTM, SimVP, and ViViT are optimized for long, dense 2D videos, not short 3D series. Their poor results may reflect mismatch rather than true inferiority.\n3. The “continuous” setting is created by subsampling ACDC; no genuinely irregular clinical series are used. Gains may arise from richer embeddings rather than true continuous modeling.", "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": "EhSrKVbj8q", "reviewer": "Reviewer_Sqka", "summary": "The paper introduces CRONOS which adapts Flow Matching to medical imaging. The main contributions are: (i) temporal broadcasting which treats multiple context scans as the source distribution and the broadcast target scan as the destination, (ii) dual formulation giving both discrete and continuous variants, and a (iii) unified framework handling multiple modalities without disease-specific assumptions.\nOverall, the paper treats the problem of predicting future 3D medical scans from multiple past observations at irregular time intervals. This is a clinically relevant problem. Most existing methods are limited to single input images and lack continuous-time predictions.", "questions": "1. Continuous vs discrete trade-offs: there appears to be inconsistencies in Table 3 and Table 2 where continuous CRONOS (Table 3) outperforms discrete version on the continuous ACDC ablation, but not necessarily on Table 2. This raises the question when is best to use continuous vs discrete alternative?\n\n2. Could you show what the performance means in terms of clinical impact ?\n\n3. How does the performance scales with the number of frames and spatial resolution ?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Problem Relevance: The paper addresses a critical problem in 3D medical imaging by proposing a unified framework for continuous sequence-to-image forecasting. \n\n2. Technical contribution: the method makes use of Flow Matching applied to the medical imaging domain through temporal broadcasting. The theoritical formulation is clear and well defined.\n\n3. Performance. CRONOS shows strong performance over LCI baseline and the spatio-temporal baselines across all three datasets.\n\n3. Evaluation: The paper proposes a comprehensive evaluation on three different datasets (ACDC, ISLES, LUMIERE) with different modalities (Cine-MRI, perfusion CT, longitudinal MRI). These experiments show good generalization capabilities of CRONOS.", "weaknesses": "1. Lack of expert validation: only voxel-wise metrics (NRMSE, PSNR, SSIM) are provided to assess performance but no clinical expert validation is shown nor other relevant anatomical metrics.\n\n2. Limited improvement: CRONOS scores 94.51% vs. LCI's 92.79% SSIM on ACDC, which appears to be a small gain given the added computational cost.\n\n3. Methodological issues: there are concerns the LOCF (Last Observed Carry Forward) filling strategy (eq 19) may introduce artifacts. Even though it is demonstrated as a key component in the ablation studies, no comparison with other approaches is shown.\n\n4. Limited discussion of failures: The paper does not provide insights into when the model might fail.", "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": "3TnzUprYxv", "reviewer": "Reviewer_EAfG", "summary": "This paper tackles the task of forecasting a 3D medical image at a future time given multiple prior 3D scans (a longitudinal series), even when the input scans have irregular timing. The authors propose CRONOS, a unified many-to-one framework that models continuous time by learning a spatio-temporal velocity field to warp all input volumes toward the target volume. This approach adapts the Flow Matching paradigm to operate directly in voxel space, enabling real-valued timestamp inputs within a single model. Experiments on three public datasets (cine MRI, perfusion CT, and longitudinal brain MRI) show that CRONOS outperforms several baseline methods in image quality metrics while using significantly less memory than diffusion-based approaches. The authors highlight that this is the first method to support multi-context continuous-time forecasting for 3D medical images, and they promise to release code and evaluation protocols for reproducibility.", "questions": "Novelty: What specific technical contributions does CRONOS introduce beyond applying standard Flow Matching to this multi-volume forecasting task? (For example, are there any new model components or training strategies, or is the contribution primarily the problem setup?)\n\nBaselines: Have the authors evaluated CRONOS against recent continuous-time or generative baselines such as STDiff (Ye & Bilodeau, 2023), LoCI-DiffCom (Zhu et al., 2024), ImageFlowNet (Liu et al., 2025), or more state-of-the-art studies? If not, what was the rationale for omitting these comparisons, and how would the authors expect CRONOS to perform relative to those methods?\n\nShared velocity field: Why was a single shared velocity field used to warp all input volumes toward the target? Did the authors consider using distinct velocity fields per context or a time-varying velocity field, and if so, how might that affect the results?\n\nContinuous-time evaluation: Can CRONOS generate predictions at arbitrary time points outside the training timestamps (for example, intermediate time interpolation or longer-term extrapolation)? If this was not tested, could the authors clarify how they expect the model to behave for times beyond the training range?\n\nUncertainty modeling: Do the authors plan to incorporate any form of uncertainty or stochasticity into CRONOS? For instance, could a probabilistic extension (e.g. a diffusion-based, VAE, or flow model) be used to capture multiple plausible future outcomes and quantify prediction confidence?\n\nGenerality beyond medical domain: Has CRONOS been evaluated on non-medical temporal imaging data (such as natural videos or other 4D sequences) to demonstrate its generality beyond the medical domain? If not, would the authors consider tempering the claims of broad applicability until such evidence is provided, or could they outline how the method might generalize to other domains?\n\nFlow field interpretability: Have the authors analyzed or visualized the learned velocity fields to assess their interpretability or biological plausibility? If not, could providing such an analysis (e.g. showing whether the predicted flow aligns with known anatomical motion or expected deformation patterns) strengthen the paper’s conclusions?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "Addresses an important, under-explored problem: The paper targets 3D medical image sequence forecasting from multiple prior scans at irregular time intervals – a challenging and clinically relevant task (e.g. disease progression) that has received limited attention.\n\nUnified continuous-time approach: CRONOS is a novel framework combining multiple-context inputs with continuous-time prediction in one model. It appears to be the first method to handle real-valued time stamps and multiple input volumes together in 3D image forecasting, filling a gap in the literature.\n\nEfficient flow-based method: The use of Flow Matching (ODE-based velocity learning) instead of iterative diffusion leads to a simpler, memory-efficient solution. CRONOS scales to long input sequences with substantially lower GPU memory usage and runtime, without needing expensive time-step sampling.\n\nStrong results on diverse datasets: The proposed model demonstrates improved performance over prior baselines (including deep video models and a strong last-scan heuristic) across three different modalities. It consistently achieves higher image similarity metrics (e.g. SSIM) on cine MRI, CT perfusion, and MRI longitudinal datasets, indicating robustness across varied medical imaging scenarios.\n\nThorough evaluation and reproducibility: The authors conduct experiments on multiple public datasets and compare against several baseline approaches. They also commit to releasing code and standardized evaluation protocols, which enhances the work’s credibility and potential impact as a benchmark for multi-context forecasting.", "weaknesses": "Limited algorithmic novelty (major): The approach offers minimal new methodology, essentially applying the existing Flow Matching paradigm to the many-to-one 3D forecasting setting without introducing new algorithmic contributions. The core idea (learning a velocity field via flow matching) is borrowed from prior work, with novelty lying primarily in its application to this domain rather than in the technique itself.\n\nMissing baseline comparisons (major): The evaluation lacks comparisons with several relevant continuous-time or generative baseline methods. Notably, recent (core-level related) approaches like STDiff (Ye & Bilodeau, 2023), LoCI-DiffCom (Zhu et al., 2024), and ImageFlowNet (Liu et al., 2025) are not included, leaving it unclear how CRONOS performs relative to the state-of-the-art in continuous video/volume forecasting.\n\nUnjustified design choice: CRONOS uses a single shared velocity field to warp all input contexts toward the target, but the paper provides no clear justification or ablation for this design. It is not explained why one global velocity field (applied to all past scans) is sufficient, as opposed to using separate or time-dependent velocity fields. This raises concerns that the model might be overly restrictive or suboptimal in capturing differing motions from each context scan.\n\nContinuous-time generalization unproven: While the method is designed for continuous time, the experiments do not explicitly validate interpolation or extrapolation to truly arbitrary time points. There is no demonstration of predicting intermediate frames between given scans or forecasting beyond the maximum training interval. Thus, the claimed continuous-time capability remains speculative, with no evidence that the model can generalize to time points outside the training distribution.\n\nDeterministic outputs (no uncertainty modeling): The framework produces a single deterministic prediction for a given input set and time, with no probabilistic modeling or uncertainty quantification. Unlike stochastic generative models (e.g. diffusion-based methods), CRONOS cannot express multiple plausible future outcomes or estimate confidence in its predictions. This lack of uncertainty modeling is a drawback for medical forecasting, where understanding predictive uncertainty is often important.\n\nGenerality claims not well-supported: The authors suggest the approach is modality-agnostic and broadly applicable, but evidence is limited to the medical imaging domain. All experiments are on medical scans; there is no validation on other data (e.g. natural video or other 4D datasets) to support the claim of general applicability. The strong generalization claims feel somewhat overstated without testing beyond the specific modalities presented.\n\nNo interpretability analysis of flows: The learned velocity fields (which are central to the method) are not analyzed or visualized in the paper. There is no examination of whether the predicted flow patterns are physically or biologically plausible. The absence of any qualitative assessment of these flows is a missed opportunity – it remains unclear if CRONOS learns meaningful motion patterns or if the velocity field could provide insights (e.g. highlighting anatomical changes or disease progression).", "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": "uEOKWe8KH6", "reviewer": "Reviewer_H1U2", "summary": "This paper focuses on temporal evolution of 3d medical imaging, given traditional works are either reliant on single prior scan or fixed grid time. Also they further make prediction on voxel level rather than traditionally global level. The method used is flow matching which learns dynamics in ODE field. Experiments on three medical imaging datasets showed improvement.", "questions": "the paper’s computational efficiency claims appear generous? While CRONOS uses less memory than ViViT (which OOMs), Table 8 shows it still uses 7–8 GB on a 40 GB GPU—more than ConvLSTM and comparable to SimVP", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The idea of continuous sequence-to-image forecasting model for 3D medical imaging is interesting, as there were few that tried to address both discrete and continuous space.\n- Demonstrates multi-context learning beyond disease-specific priors. It seems to generalize to different dataset types (cardiac, stroke, tumor).", "weaknesses": "- The temporal model feels suboptimal. For continuous setting they compute time conditioning as the mean of Fourier features: $\\text{Enc}(t)=\\frac{1}{T}\\sum_{i=1}^T\\gamma(t_i)$ and inject via FiLM. But averaging removes ordering and emphasizes the centroid of context times, not the relative spacing or which context frame is earlier/later. Two very different temporal configurations (e.g., times [0,1,10] vs [4,5,6]) can have similar mean embeddings but imply dramatically different dynamics. Time information relevant for rate estimation is the vector of deltas $\\{t_{\\text{target}}-t_i\\}$, not the mean. The current encoding conflates sequences of varying lengths and spacing. So model may ignore order and rely more on spatial cues; can fail when relative timing matters (e.g., when early vs late context frames carry different predictive value).\n- they stack T context volumes into $X_0=[I_1,\\dots,I_T]$ and broadcast $I_{\\text{target}} to X_1$. The training target in velocity space is always $I_{\\text{target}}-I$ (element-wise per-channel difference), i.e., the same subtraction applied to each context channel. Different context frames correspond to different $\\Delta t_i$. Using the same raw difference $I_{\\text{target}}-I_i$ as a per-channel supervision makes the network learn different displacements for each channel that are unrelated to any consistent per-channel dynamics. This places the burden on $v_\\theta$ to internally down-weight or rescale channels based on timestamps—again brittle and underconstrained.\n- Overall one major concern would be whether continuous-time modeling actually adds value beyond what a well-tuned discrete model with adaptive interpolation can achieve. Why not simply use a dense-grid discrete model with a learned interpolation kernel", "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)