ChronoFlow: Hierarchical Flow Matching for Irregular Time Series Generation

Changhun Kim; Sunguk Jang; Jeongjun Lee; Juhwan Choi; Sangchul Hahn; Grigorios Chrysos; Eunho Yang; Juho Lee

cs.AISep 27, 2026

ChronoFlow: Hierarchical Flow Matching for Irregular Time Series Generation

Authors: Changhun Kim, Sunguk Jang, Jeongjun Lee, Juhwan Choi, Sangchul Hahn, Grigorios Chrysos, Eunho Yang, Juho Lee

Organizations: University of Wisconsin–Madison · AITRICS · KAIST

Abstract

Recent advances in generative modeling have substantially improved time series generation, yet most existing methods either assume a regular temporal grid or focus on feature dynamics under a given sampling structure. This makes them illsuited for generating irregular time series in their native form, where a model must capture not only feature values, but also how many observations occur, when they occur, and which features are observed together. To address this heterogeneous generation problem, we propose ChronoFlow, a unified hierarchical flow matching framework organized by statistical granularity. Following a coarse-to-fine hierarchy, ChronoFlow first generates observation counts and feature-wise frequencies, then jointly generates observation times and feature co-observation patterns, and finally generates values conditioned on the realized pattern. This turns a complex joint generation problem into structurally aligned subproblems while preserving their dependencies. To evaluate complete irregular time series generation, we introduce complementary metrics spanning sample realism, sampling structure, value fidelity, and temporal and cross-feature dependencies, and validate them through controlled corruptions. Across five benchmarks, ChronoFlow achieves strong improvements in generation fidelity over existing baselines, while factorization studies support the proposed hierarchy. Our code is available at https://anonymous.4open.science/r/ChronoFlow.

Figures & tables

Figure 1: Overview of ChronoFlow for irregular time series generation. IntensityFlow generates global statistics, PatternFlow joint times and panels, and ValueFlow conditional values. The feature-by-time display is

\bm{B}^{\top}

. Figure notation

s

z_{I}

, and

P

corresponds to flow time

t

, state

\bm{u}

, and pattern

(\bm{\tau},\bm{B})

Dataset	Model	Set-Discr. $\downarrow$	CoOb $\downarrow$	Pattern-MMD 2 $\downarrow$	Trans-MMD 2 $\downarrow$	Value-W1 $\downarrow$	Set-Corr. $\downarrow$
eICU	Oracle	0.0019 $\pm$ 0.0012	0.0306 $\pm$ 0.0155	0.0000 $\pm$ 0.0000	0.0004 $\pm$ 0.0001	0.0312 $\pm$ 0.0007	0.0364 $\pm$ 0.0015
	Poisson + LatentODE	0.4242 $\pm$ 0.0317	1.9710 $\pm$ 0.0017	0.0047 $\pm$ 0.0024	0.0249 $\pm$ 0.0038	0.2216 $\pm$ 0.0321	0.0643 $\pm$ 0.0049
	LogNormMix + mTAN	0.4555 $\pm$ 0.0021	0.0383 $\pm$ 0.0141	0.0011 $\pm$ 0.0015	0.0169 $\pm$ 0.0025	0.2910 $\pm$ 0.0319	0.0813 $\pm$ 0.0060
	LogNormMix + TFM	0.4518 $\pm$ 0.0122	0.0374 $\pm$ 0.0042	0.0014 $\pm$ 0.0019	0.0247 $\pm$ 0.0071	0.3585 $\pm$ 0.0321	0.1435 $\pm$ 0.0071
	FlexTPP	0.3629 $\pm$ 0.0288	0.1336 $\pm$ 0.1033	0.0032 $\pm$ 0.0014	0.0070 $\pm$ 0.0030	0.1081 $\pm$ 0.0396	0.0532 $\pm$ 0.0112
	ChronoFlow	0.0995 $\pm$ 0.0098	0.0380 $\pm$ 0.0047	0.0002 $\pm$ 0.0001	0.0045 $\pm$ 0.0002	0.0504 $\pm$ 0.0047	0.0385 $\pm$ 0.0003

Table 1: Generation fidelity across five irregular time series benchmarks. We compare ChronoFlow with four baselines using six complementary metrics covering overall sample realism, sampling structure, temporal dynamics, value fidelity, and cross-feature dependencies. Oracle denotes a real–real reference. Bold indicates the lowest mean among generators for each dataset and metric.

Model	Process	Size	Set-Discr. $\downarrow$	CoOb $\downarrow$	Pattern-MMD 2 $\downarrow$	Trans-MMD 2 $\downarrow$	Value-W1 $\downarrow$	Set-Corr. $\downarrow$
Oracle	–	–	0.0019 $\pm$ 0.0012	0.0306 $\pm$ 0.0155	0.0000 $\pm$ 0.0000	0.0004 $\pm$ 0.0001	0.0312 $\pm$ 0.0007	0.0364 $\pm$ 0.0015
Value $\to$ Pattern	$M\to\mathbf{x}\to(\bm{\tau},\bm{B})$	2.70M	0.4511 $\pm$ 0.0217	0.2354 $\pm$ 0.0098	0.0051 $\pm$ 0.0001	0.0099 $\pm$ 0.0003	0.1142 $\pm$ 0.0022	0.0461 $\pm$ 0.0046
Joint TPV	$M\to(\bm{\tau},\bm{B},\mathbf{x})$	1.12M	0.2639 $\pm$ 0.0039	0.0867 $\pm$ 0.0033	0.0008 $\pm$ 0.0002	0.0275 $\pm$ 0.0013	0.3179 $\pm$ 0.0044	0.0698 $\pm$ 0.0101
Joint All	$(M,\bm{\tau},\bm{B},\mathbf{x})$	2.21M	0.2445 $\pm$ 0.1387	0.0731 $\pm$ 0.0055	0.0018 $\pm$ 0.0002	0.0074 $\pm$ 0.0009	0.0779 $\pm$ 0.0011	0.0423 $\pm$ 0.0012
w/o OT	$(M,\bm{r})\to(\bm{\tau},\bm{B})\to\mathbf{x}$	2.06M	0.4316 $\pm$ 0.0085	0.0854 $\pm$ 0.0042	0.0382 $\pm$ 0.0031	0.0083 $\pm$ 0.0004	0.0731 $\pm$ 0.0038	0.0382 $\pm$ 0.0037
ChronoFlow	$(M,\bm{r})\to(\bm{\tau},\bm{B})\to\mathbf{x}$	2.06M	0.0995 $\pm$ 0.0098	0.0380 $\pm$ 0.0047	0.0002 $\pm$ 0.0001	0.0045 $\pm$ 0.0002	0.0504 $\pm$ 0.0047	0.0385 $\pm$ 0.0003

Table 2: Ablation study of ChronoFlow on eICU. We compare alternative generation factorizations and evaluate the effect of optimal-transport coupling in PatternFlow.

M

is the number of observation occasions and

\bm{r}

contains feature-wise observation frequencies.

\bm{\tau}

denotes observation times,

\bm{B}

feature panels, and

\mathbf{x}

feature values.

Figure 2: Qualitative analysis on eICU. Top: real and generated samples from LogNormMix + mTAN, FlexTPP, and ChronoFlow. Bottom: ground-truth versus ChronoFlow distributions of observation counts, feature co-observation, and Heart Rate and Temperature values.

Figure 3: Further analysis. (a,b) eICU latency–fidelity and ODE-step sensitivity, with bubble size indicating parameter count in (a). (c) Designated-corruption responses normalized by endpoint change within each dataset, then averaged across five datasets. Shading is between-dataset sample standard deviation. (d) Relative positive responses across corruptions, averaged over available datasets. Definitions and missing-support exceptions are in Section D.7 .

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

\bm{\tau}_{t_{P}}\leftarrow(1-t_{P})\bm{\tau}_{0}+t_{P}\bm{\tau}_{1},\qquad\bm{B}_{t_{P}}\leftarrow(1-t_{P})\bm{B}_{0}+t_{P}\bm{B}_{1}

Appendix

Algorithm 1 Training procedure for ChronoFlow.

(\bar{\bm{\tau}},\bar{\bm{B}})\leftarrow\Phi_{\mathrm{ODE}}\left(v_{\theta_{P}},(\bm{\tau}_{0},\bm{B}_{0});0\!\rightarrow\!1\mid\hat{M},\hat{\bm{r}}\right)

Appendix

Algorithm 2 Sampling procedure for ChronoFlow.

	eICU	P12	MIMIC-III	MIMIC-IV	Activity
# Features	11	35	28	28	12
Time Window	24h	48h	48h	48h	2.28s
Min Resolution	1m	1m	1m	1m	10ms
Max Measurements ( $N_{\max}$ )	672	1,024	1,024	1,024	600
Train (Neg / Pos)	13,817 / 1,346	6,579 / 1,093	10,655 / 1,611	13,806 / 2,046	2,860
Val (Neg / Pos)	3,454 / 336	1,645 / 273	2,662 / 404	3,452 / 512	471

Appendix

Table A3: Dataset statistics for the five irregular time series benchmarks. Clinical split sizes are reported as negative/positive outcome counts, while Activity split sizes indicate the total number of windows across its seven activity classes.

N_{\max}

is the measurement budget, not the number of observation occasions.

Model	$(M,\bm{r})$	$(\bm{\tau},\bm{B})$	$\mathbf{x}$	Set-Discr. $\downarrow$	CoOb $\downarrow$	Pattern-MMD 2 $\downarrow$	Trans-MMD 2 $\downarrow$	Value-W1 $\downarrow$	Set-Corr. $\downarrow$
Oracle	GT	GT	GT	0.0019 $\pm$ 0.0012	0.0306 $\pm$ 0.0155	0.0000 $\pm$ 0.0000	0.0004 $\pm$ 0.0001	0.0312 $\pm$ 0.0007	0.0364 $\pm$ 0.0015
Stage-wise Oracle Intervention
ChronoFlow	sampled	sampled	sampled	0.0995 $\pm$ 0.0098	0.0380 $\pm$ 0.0047	0.0002 $\pm$ 0.0001	0.0045 $\pm$ 0.0002	0.0504 $\pm$ 0.0047	0.0385 $\pm$ 0.0003
+ GT $(M,\bm{r})$	GT	sampled	sampled	0.0153 $\pm$ 0.0140	0.0128 $\pm$ 0.0011	0.0000 $\pm$ 0.0000	0.0040 $\pm$ 0.0002	0.0481 $\pm$ 0.0037	0.0365 $\pm$ 0.0022
+ GT $(M,\bm{r})$ , $(\bm{\tau},\bm{B})$	GT	GT	sampled	0.0928 $\pm$ 0.1521	0.0000 $\pm$ 0.0000	0.0000 $\pm$ 0.0000	0.0003 $\pm$ 0.0002	0.0508 $\pm$ 0.0100	0.0358 $\pm$ 0.0019
Robustness to Upstream Perturbations

Appendix

Table A4: Stage-wise oracle intervention and perturbation analysis of ChronoFlow on eICU. At inference, generated upstream variables are replaced by their ground-truth counterparts to assess sensitivity to upstream conditioning. We further perturb ground-truth upstream variables with relative noise of severity

s

to evaluate downstream robustness; ground-truth variables are taken from the evaluated test samples, so these rows can fall below the real–real reference.

(M,\bm{r})

denotes global observation statistics,

(\bm{\tau},\bm{B})

the sampling pattern, and

\mathbf{x}

the feature values.

Model	Optimizer	LR setting	Schedule
Poisson + LatentODE	Adamax	$10^{-2}$	Exponential decay
LogNormMix + mTAN (Pattern)	Adam	$2\times 10^{-4}$	Constant
LogNormMix + mTAN (Value)	Adam	$2\times 10^{-3}$	Constant
LogNormMix + TFM	Adam	$2\times 10^{-4}$	Constant
FlexTPP	AdamW	$5\times 10^{-4}$	One-cycle
ChronoFlow	Adam	$4\times 10^{-5}$	Warmup + plateau

Appendix

Table A5: Optimization settings for the evaluated eICU checkpoints. The listed learning rate is the peak rate for FlexTPP and the configured base rate for ChronoFlow. ChronoFlow uses a warmup target of

8\times 10^{-4}

and a minimum learning rate of

10^{-5}

Figure A4: UMAP visualizations of real and generated samples across the five benchmarks: eICU, P12, MIMIC-III, MIMIC-IV, and Activity, shown from top to bottom. For each dataset, the panels compare the real-data representation with samples generated by Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow. Overlap is interpreted qualitatively, as two-dimensional projection can hide discrepancies.

Figure A5: Qualitative comparison of baseline methods and ChronoFlow on the eICU benchmark. For this dataset, rows correspond to Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. For each model, (a) shows the distribution of the total number of observations per stay. Panel (b) shows feature co-observation rates for all 11 features. The lower triangle shows ground truth, the upper triangle shows generated samples, and the diagonal shows ground-truth marginals. Panels (c, d) show value distributions of the most frequent feature and the median-frequency feature.

Figure A6: Qualitative comparison of baseline methods and ChronoFlow on the P12 benchmark. For this dataset, rows correspond to Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. For each model, (a) shows the distribution of the total number of observations per stay. Panel (b) shows feature co-observation rates for the 12 most frequent features. The lower triangle shows ground truth, the upper triangle shows generated samples, and the diagonal shows ground-truth marginals. Panels (c, d) show value distributions of the most frequent feature and the median-frequency feature.

Figure A7: Qualitative comparison of baseline methods and ChronoFlow on the MIMIC-III benchmark. For this dataset, rows correspond to Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. For each model, (a) shows the distribution of the total number of observations per stay. Panel (b) shows feature co-observation rates for the 12 most frequent features. The lower triangle shows ground truth, the upper triangle shows generated samples, and the diagonal shows ground-truth marginals. Panels (c, d) show value distributions of the most frequent feature and the median-frequency feature.

Figure A8: Qualitative comparison of baseline methods and ChronoFlow on the MIMIC-IV benchmark. For this dataset, rows correspond to Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. For each model, (a) shows the distribution of the total number of observations per stay. Panel (b) shows feature co-observation rates for the 12 most frequent features. The lower triangle shows ground truth, the upper triangle shows generated samples, and the diagonal shows ground-truth marginals. Panels (c, d) show value distributions of the most frequent feature and the median-frequency feature.

Figure A9: Qualitative comparison of baseline methods and ChronoFlow on the Activity benchmark. For this dataset, rows correspond to Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. For each model, (a) shows the distribution of the total number of observations per window. Panel (b) shows feature co-observation rates for the 12 most frequent features. The lower triangle shows ground truth, the upper triangle shows generated samples, and the diagonal shows ground-truth marginals. Panels (c, d) show value distributions of the most frequent feature and the median-frequency feature.

Figure A10: Qualitative comparison of generated samples on the eICU benchmark. Rows correspond to ground truth, Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. Each row shows four samples. Colors indicate standardized feature values, and the total number of observations is shown above each sample.

Figure A11: Qualitative comparison of generated samples on the P12 benchmark. Rows correspond to ground truth, Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. Each row shows four samples. Colors indicate standardized feature values, and the total number of observations is shown above each sample.

Figure A12: Qualitative comparison of generated samples on the MIMIC-III benchmark. Rows correspond to ground truth, Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. Each row shows four samples. Colors indicate standardized feature values, and the total number of observations is shown above each sample.

Figure A13: Qualitative comparison of generated samples on the MIMIC-IV benchmark. Rows correspond to ground truth, Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. Each row shows four samples. Colors indicate standardized feature values, and the total number of observations is shown above each sample.

Figure A14: Qualitative comparison of generated samples on the Activity benchmark. Rows correspond to ground truth, Poisson + LatentODE, LogNormMix + mTAN, LogNormMix + TFM, FlexTPP, and ChronoFlow, respectively. Each row shows four samples. Colors indicate standardized feature values, and the total number of observations is shown above each sample.

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