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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
TL;DR
Irregular time series generation requires modeling observation counts, times, and feature co-observation as well as values, whereas many existing approaches assume regular grids or given sampling structures. ChronoFlow hierarchically generates global statistics, sampling patterns, and conditioned values, and its evaluation covers complete samples. Across five benchmarks, it achieves the lowest mean among generators in most dataset–metric comparisons.
Problem
Many time series generators assume regular grids or focus on feature dynamics under a given sampling structure, while irregular samples also vary in observation counts, timing, and feature co-observation.
Source: §1 · pp. 1–2Method
ChronoFlow hierarchically generates observation counts and feature-wise frequencies, jointly generates observation times and feature co-observation patterns, then generates values conditioned on the realized pattern.
Source: §1 · p. 2Results
Takeaways & Limitations
The evaluation protocol combines complementary diagnostics of sampling structure and value fidelity, with controlled corruptions assessing their sensitivity.
Source: §1 · p. 2The de-identified EHR datasets contain sensitive health information; generated samples may inherit source-data biases or sensitive patterns and should not be assumed to provide formal privacy guarantees or support clinical decision-making without further validation.
Source: ETHICS STATEMENT · p. 10
Abstract
from arXiv · showhide
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.
1 INTRODUCTION
Irregular time series generation must model observation counts, timing, and feature co-observation as well as values. ChronoFlow addresses this with hierarchical generation and an evaluation protocol for complete samples; experiments across five benchmarks report strong fidelity results.
1 INTRODUCTION
- Irregular samples require modeling how many observations occur, when they occur, and which features are observed together, in addition to their values.Measurements may be asynchronous and unevenly spaced, as in electronic health records and physiological sensing.Source: §1 · pp. 1–2
- ChronoFlow generates global observation statistics, then jointly generates observation times and feature co-observation patterns, and finally generates values conditioned on the realized pattern.The hierarchical conditioning is intended to preserve dependencies across these stages.Source: §1 · p. 2
- The evaluation protocol spans sample realism, sampling structure, value fidelity, temporal dynamics, and cross-feature dependencies, with metric sensitivity assessed through controlled corruptions.It addresses evaluation of complete generated samples rather than only missing-value interpolation or future-value prediction.Source: §1 · p. 2
- Across five benchmarks, ChronoFlow achieves state-of-the-art generation fidelity across most datasets and metrics.Factorization studies on eICU and oracle interventions examine the hierarchy and its sensitivity to upstream errors.Source: §1 · p. 2
2 RELATED WORK
Prior work addresses parts of irregular time series generation, including continuous-time values, observation times, event sequences, and pattern-to-value generation. ChronoFlow distinguishes itself through explicit occasion–panel representation and an evaluation protocol for complete irregular samples.
Time series and irregular-trajectory generation
- TimeGAN, Diffusion-TS, and FlowTS generate on shared temporal grids, while ImagenI2R learns from irregular samples but generates regular sequences.TimEHR generates missingness masks followed by conditional values; mTAN predicts values at supplied times, while TFM models continuous trajectories and predicts the next observation time.Source: §2 · p. 2
Observation-process and event generation
- ChronoFlow's distinction is an explicit occasion–panel representation with global count and feature-frequency conditioning, joint time–panel generation, and conditional values.The formulation and evaluation are the contribution; the framework uses established flow matching and attention components.Source: §2 · p. 2
Evaluation of full irregular samples
- The evaluation protocol organizes comparisons around complete irregular samples and combines diagnostics of counts, timing, co-observation, and value dependencies.Controlled corruptions probe the diagnostics' sensitivity.Source: §2 · p. 3
3 PROPOSED METHOD: CHRONOFLOW
ChronoFlow represents each irregular sample with observation times, feature panels, and observed values, then factorizes generation by statistical granularity. Flow matching provides a shared generative principle, while three conditioned stages generate global statistics, sampling patterns, and values.
3 PROPOSED METHOD: CHRONOFLOW
- ChronoFlow factorizes the augmented variables (M, r, S) by statistical granularity, from global statistics to occasion-level patterns and measurement-level values.During generation, sampled (M, r) condition the generation of S and are then discarded; decoded panels need not reproduce r exactly.Source: §3 · p. 3
3.1 BACKGROUND: FLOW MATCHING
- All three stages use flow matching, which interpolates between a noise sample and a data sample with a linear path and target velocity.After training, samples are generated by solving the learned dynamics from a noise sample.Source: §3.1 · p. 3
3.2 HIERARCHICAL ARCHITECTURE OF CHRONOFLOW
- IntensityFlow generates global observation statistics (M, r), using a dataset-specific upper bound for M and a lightweight MLP for the fixed-dimensional summary.At inference, M is rounded to an integer and each feature frequency is projected onto {0, 1/M, . . . , 1}.Source: §3.2 · p. 3
- PatternFlow jointly generates observation times and feature panels conditioned on (M, r), so their current states can inform each other during generation.One-dimensional optimal-transport assignment sorts the time endpoints and applies the corresponding permutations to panels; it minimizes squared temporal assignment cost, without claiming optimality for the joint time–panel distribution.Source: §3.2 · p. 4
- ValueFlow generates values conditioned on the realized pattern, representing active measurements as event tokens whose feature identity, time, and noisy value can interact through a Set Transformer.Shared embeddings without index-dependent positional encodings make ValueFlow equivariant to event-token permutations.Source: §3.2 · pp. 4–5
4 EVALUATION METRICS FOR IRREGULAR TIME SERIES GENERATION
The section evaluates complete irregular samples with complementary diagnostics because conditional interpolation or extrapolation alone does not assess both observation patterns and values. Its metrics cover full-sample distinguishability, sampling-pattern fidelity, and value fidelity and dependencies.
4 EVALUATION METRICS FOR IRREGULAR TIME SERIES GENERATION
- Six complementary diagnostics assess complete irregular samples across sample realism, sampling structure, marginal values, and temporal and cross-feature dependencies.The protocol combines established statistical comparisons and controlled-corruption sensitivity checks.Source: §4 · p. 5
4.1 FULL-SAMPLE DISTINGUISHABILITY
- Set-Discr. measures held-out accuracy deviation from chance for a permutation-invariant classifier distinguishing real and generated samples using times, feature identities, and values.A low score indicates difficulty for this trained classifier, not equality of the underlying distributions.Source: §4.1 · p. 5
4.2 SAMPLING-PATTERN FIDELITY
- CoOb. compares pairwise co-observation frequencies in common time bins, while Pattern-MMD2 assesses feature-wise counts and timing beyond pairwise co-observation.Pattern-MMD2 sums Fourier time features without normalizing by feature observation count; summary magnitude reflects counts, and components summarize timing at the selected Fourier resolution.Source: §4.2 · pp. 5–6
4.3 VALUE FIDELITY AND DEPENDENCIES
- Value-W1 compares per-feature empirical value distributions, Trans-MMD2 assesses local value transitions with elapsed times, and Set-Corr compares proximity-weighted correlations for asynchronous feature pairs.Value-W1 does not assess value ordering or dependence on observation patterns; Set-Corr's comparison depends on pair coverage, and all scores are lower-is-better, complementary, and non-exhaustive.Source: §4.3 · p. 6
5 EXPERIMENTS
The experiments evaluate complete irregular time-series generation across five benchmarks, then examine the hierarchy, upstream-error sensitivity, and metric behavior. ChronoFlow has the lowest mean in most dataset–metric comparisons, while results also show trade-offs and scope boundaries.
5.1 EXPERIMENTAL SETUP
- The setup compares ChronoFlow with four baselines and uses test-set-sized samples, training-only metric calibration, and three independently trained models.The reported mean ± sample standard deviation is across three seeds; bold marks the lowest generator mean, not a significance test.Source: §5.1 · p. 7
5.2 MAIN RESULTS
- ChronoFlow has the lowest mean in 21 of 30 dataset–metric comparisons across five benchmarks.Table 1 covers six complementary metrics; the reported lead is broad but not universal.Source: §5.2 · p. 7, Table 1 · p. 7
- On eICU, generated samples reproduce observation-count, co-observation, and value distributions, including frequent IBP Dia.–IBP Sys. co-observation.The samples also show grouped observations, irregular temporal gaps, and feature-specific sparsity similar to real data.Source: §5.2 · p. 8, Figure 2 · p. 8
5.3 ABLATION STUDY
- On eICU, ChronoFlow has lower means across all six metrics than the tested joint and reverse-order factorizations, though capacity and conditioning differ.Removing optimal-transport coupling worsens Pattern-MMD2 from 0.0002 to 0.0382 and Set-Discr. from 0.0995 to 0.4316.Source: §5.3 · pp. 8–9, Table 2 · p. 8
5.4 ERROR PROPAGATION ANALYSIS
- Ground-truth global observation statistics reduce eICU Set-Discr. from 0.0995 to 0.0153 and CoOb from 0.0380 to 0.0128, but effects vary by metric.With ground-truth sampling patterns, temporal-transition fidelity approaches the empirical real–real reference; Set-Discr. remains variable and Value-W1 changes little.Source: §5.4 · p. 9
- On eICU, stronger perturbations to global statistics worsen CoOb and Trans-MMD2, while Value-W1 stays between 0.0460 and 0.0600.Perturbing the sampling pattern further increases CoOb discrepancies.Source: §5.4 · p. 9
5.5 FURTHER EVALUATION
- On eICU, ChronoFlow has lower Set-Discr. and latency than FlexTPP and LogNormMix + TFM, while two faster baselines are more distinguishable.Increasing integration steps from 10 to 50 reduces Set-Discr. from 0.1983 to 0.0912 and Value-W1 from 0.1048 to 0.0534; both change little across 50–500 steps.Source: §5.5 · p. 9
- Across five datasets, normalized metric responses increase with designated corruption severity, but these relative responses are neither absolute calibration nor exclusive sensitivity.Value-W1 and Set-Corr. mainly respond to their designated corruptions; count dropout also affects CoOb and Trans-MMD2.Source: §5.5 · p. 9
6 CONCLUSION
The conclusion presents ChronoFlow as hierarchical generation for complete irregular samples, with evaluation spanning sampling structure and value fidelity. Benchmark results support structured generation within the tested settings.
6 CONCLUSION
- ChronoFlow formulates complete irregular samples through observation occasions and feature panels, then generates them hierarchically.The hierarchy organizes the joint problem by statistical granularity while preserving dependencies.Source: §6 · p. 9
- The evaluation combines complementary diagnostics of sampling structure and value fidelity, with sensitivity assessed through controlled corruptions.Figure 3 further analyzes latency–fidelity, ODE-step sensitivity, and corruption responses averaged across datasets.Source: §6 · p. 9, Figure 3 · p. 10
- Across five benchmarks, ChronoFlow has the lowest mean among generators in most dataset–metric comparisons; eICU factorization studies support the proposed hierarchy.The conclusion limits this support to the tested settings.Source: §6 · p. 9
AI USE STATEMENT
The authors disclose AI assistance across research, experiments, and manuscript preparation, alongside independent review and responsibility for the final work.
AI USE STATEMENT
- Generative AI tools assisted with implementing research ideas and verifying theoretical arguments and proofs.The authors state that all AI-assisted outputs were independently reviewed and verified.Source: AI USE STATEMENT · p. 10
- AI tools also assisted with designing and implementing experiments.The authors take full responsibility for the final content.Source: AI USE STATEMENT · p. 10
- AI tools assisted with polishing the manuscript, with the authors retaining responsibility for its final content.The statement says all AI-assisted outputs were independently reviewed and verified.Source: AI USE STATEMENT · p. 10
ETHICS STATEMENT
The ethics statement identifies the use of de-identified EHR benchmarks and cautions that generated samples may retain sensitive patterns or biases.
ETHICS STATEMENT
- The study uses four de-identified EHR benchmarks: eICU, PhysioNet-2012, MIMIC-III, and MIMIC-IV.MIMIC-III, MIMIC-IV, and eICU are handled under the PhysioNet Credentialed Health Data Use Agreement.Source: ETHICS STATEMENT · p. 10
- Despite de-identification, the datasets contain sensitive health information, and generated samples may inherit source-data biases or sensitive patterns.The statement cautions against assuming formal privacy guarantees.Source: ETHICS STATEMENT · p. 10
- Generated samples should not be assumed to support clinical decision-making without further validation.The statement does not claim formal privacy guarantees.Source: ETHICS STATEMENT · p. 10
A LIMITATIONS AND FUTURE WORK
The appendix identifies limitations in discrete structure, conditioning, resolution, value support, scalability, and evaluation scope. It also records the training and inference sequence and gives proofs for temporal coupling and ValueFlow permutation equivariance.
A LIMITATIONS AND FUTURE WORK
- Continuous relaxations and thresholding may poorly represent discrete structure, sampled frequencies need not agree with decoded panels, and downstream stages face a train–inference conditioning shift.Discrete flow matching and consistency-preserving decoding are proposed extensions; eICU interventions diagnose but do not resolve the shift.Source: A LIMITATIONS AND FUTURE WORK · p. 13
- The clinical timestamps have finite resolution, continuous value generation does not enforce ordinal or feature-specific support, and attention scales quadratically with occasion and measurement counts.Longer, denser records, broader comparisons and ablations, and evaluation of downstream utility, privacy, and memorization remain outside the evidence; factorization ablations are limited to eICU.Source: A LIMITATIONS AND FUTURE WORK · p. 13
B ALGORITHMS
- Training optimizes all three flow-matching models simultaneously with ground-truth upstream conditions, while inference sequentially generates global statistics, sampling structure, and then values.The appendix assigns detailed procedures to Algorithms 1 and 2.Source: B ALGORITHMS · p. 13
C.1 TEMPORAL OPTIMAL-TRANSPORT ASSIGNMENT
- Sorting the two time sequences and applying the same permutations to panels gives a minimum-cost one-dimensional temporal assignment; ties can leave multiple minimizers with the same minimum cost.Removing any inversion does not increase transport cost, and repeated removals yield the sorted-to-sorted assignment.Source: §C.1 · pp. 13–14
C.2 PERMUTATION EQUIVARIANCE OF VALUEFLOW
- ValueFlow is permutation equivariant over event tokens because its tokenization and Transformer operations preserve event-token permutations while register tokens remain fixed.The proof uses shared token embeddings without index-dependent positional encodings.Source: §C.2 · pp. 14–15
D DETAILS OF EVALUATION METRICS
- The evaluation appendix defines six complementary metrics for complete-sample distinguishability, sampling-pattern fidelity, and value fidelity and dependencies.It specifies a common evaluation protocol and MMD estimator before detailing the metrics.Source: D DETAILS OF EVALUATION METRICS · p. 15
D.1 EVALUATION REPRESENTATION AND PROTOCOL
The evaluation uses benchmark-resolution coordinates and fixed calibration procedures to compare generated samples with test data. Its complementary metrics and controlled corruptions assess distinct fidelity aspects, with stated limits on interpretation.
D.1 EVALUATION REPRESENTATION AND PROTOCOL
- Evaluation maps benchmark time indices to normalized coordinates, but does not establish fidelity below the benchmark resolution.Metrics use preprocessed windows and masks; observed zeros remain valid measurements.Source: §D.1 · pp. 15–16
D.2 COMMON MMD ESTIMATOR
- The common Gaussian-kernel MMD estimator uses training-calibrated bandwidths, and clipped negative estimates reported as zero do not establish equal distributions.Bandwidths use the median positive pairwise distance from calibration data, with σ = 1 as fallback when none is positive.Source: §D.2 · p. 16
D.3 FULL-SAMPLE DISTINGUISHABILITY
- Set-Discr trains a permutation-invariant binary classifier on complete samples’ observation times, feature identities, and values to assess real–generated distinguishability.A low score concerns the specified classifier and training procedure.Source: §D.3 · pp. 16–17
D.4 SAMPLING-PATTERN FIDELITY
- CoOb compares real and generated feature co-observation frequencies within time bins, while Pattern-MMD2 compares feature-wise observation frequency and timing across samples.CoOb uses one-minute bins for clinical benchmarks and 10 ms bins for Activity; Pattern-MMD2 uses fixed sampled frequencies and retains frequency and timing information.Source: §D.4 · p. 17
D.5 VALUE FIDELITY AND DEPENDENCIES
- Value-W1, Trans-MMD2, and Set-Corr assess marginal values, consecutive-observation dynamics, and asynchronously observed cross-feature dependencies, respectively.Set-Corr excludes pairs invalid in either collection, so it alone cannot establish preservation of all feature dependencies.Source: §D.5 · pp. 17–18
D.6 INTERPRETATION AND VALIDATION
- The six metrics provide complementary, non-exhaustive diagnostics; value metrics on generated patterns can reflect sampling and value-generation errors, and finite pattern embeddings may emphasize count changes over some timing changes.The corruption tests do not exhaustively assess sampling–value dependence, downstream utility, or memorization.Source: §D.6 · p. 18
D.7 CONTROLLED-CORRUPTION PROTOCOL
- Controlled corruptions target count dropout, co-observation shifts, time jitter, value noise, and cross-feature shuffling, with designated metrics and severity levels.Sensitivity curves use shared zero-severity baselines and average across datasets; normalized corruption profiles describe relative responses within metrics, not comparable absolute sensitivity.Source: §D.7 · p. 19
E.1 DETAILS OF DATASETS
The experiments use four clinical datasets and Activity, with explicit observation masks and filtering that delimit the evaluated records. The appendix details generation, baselines, and optimization procedures.
E.1 DETAILS OF DATASETS
- The benchmarks comprise four clinical datasets and the non-clinical Human Activity dataset, evaluated against test partitions using their observation windows and masks.Clinical records with observations at more than half of the window’s time indices are excluded, so results do not establish performance on those unusually dense records.Source: §E.1 · p. 20
E.2 DETAILS OF GENERATION
- ChronoFlow generates global observation statistics, then times and feature panels, then values conditioned on the sampling pattern; its default uses 100 ODE steps per flow module.The listed eICU factorization configurations differ in capacity and conditioning, and do not isolate every factorization choice; oracle interventions change downstream conditioning while keeping the trained model fixed.Source: §E.2 · pp. 20–21
F DETAILS OF BASELINES
- The full-generation comparison includes four baselines, with sampling-pattern generators paired with value models where needed and FlexTPP adapted for event-sequence generation.The comparison is unconditional: baselines receive no test observations, timestamps, or masks.Source: F DETAILS OF BASELINES · pp. 21–22
F.1 HYPERPARAMETER OPTIMIZATION
- Baseline learning rates were screened on eICU using validation mean rank across preliminary metrics, then selected settings were used in final baseline runs.Screening used 256 generated samples, fewer than the test-set-sized samples used for main results.Source: §F.1 · p. 22
G VISUALIZATION OF GENERATED SAMPLES
The appendix supplements quantitative fidelity results with qualitative projections, aggregate distribution comparisons, and individual generated samples across the five benchmarks. These visualizations are illustrations rather than distributional tests.
G VISUALIZATION OF GENERATED SAMPLES
- UMAP panels compare real-data representations with samples from five generators across eICU, P12, MIMIC-III, MIMIC-IV, and Activity; apparent overlap is qualitative and may hide discrepancies.The visualization uses a single-seed illustration, not a three-seed performance average, and is not evidence against memorization.Source: G VISUALIZATION OF GENERATED SAMPLES · p. 23, Figure A4 · p. 24
- Figures A5–A9 compare observation-count distributions, feature co-observation rates, and value distributions for baseline methods and ChronoFlow across the five benchmarks.For co-observation panels, the lower triangle is ground truth, the upper triangle generated samples, and the diagonal ground-truth marginals.Source: Figure A5 · p. 25, Figure A6 · p. 26, Figure A7 · p. 27
- Figures A10–A14 show four samples per method and benchmark, with standardized feature values encoded by color and total observation counts displayed above each sample.Rows list ground truth followed by the baseline methods and ChronoFlow.Source: Figure A10 · p. 30, Figure A11 · p. 31, Figure A12 · p. 32