MarkovTS: Pretrained State-Transition Representations for Zero-Shot Time Series Generation

Yujie Li; Zezhi Shao; Jingbo Zhou; Yongjun Xu; Xueqi Cheng; Fei Wang

cs.LGOct 31, 2026

MarkovTS: Pretrained State-Transition Representations for Zero-Shot Time Series Generation

Authors: Yujie Li, Zezhi Shao, Jingbo Zhou, Yongjun Xu, Xueqi Cheng, Fei Wang

Organizations: State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Baidu Frontier Research Department, Beijing, China

Abstract

Across heterogeneous real-world domains, time-series generation supports simulation, model development, and data augmentation by generating sequences that preserve target-domain statistics and temporal dependencies when real observations are scarce or costly. However, existing methods predominantly address in-domain generation, limiting their reuse in unseen domains. We study reference-conditioned zero-shot time series generation: target domains are unseen during pretraining, generation uses a single target-domain reference sequence, and no model parameters are updated. MarkovTS characterizes sequence evolution through local morphologies and their ordered transitions at multiple temporal scales. Its pretrained encoder quantizes normalized time-series patches into multiscale morphological states with a state codebook, while a transition codebook encodes contextual transitions between adjacent intervals. These transferable state-transition representations condition a pretrained flow-matching model. At generation, the frozen model combines a reference-derived condition with independent Gaussian noise to produce stochastic samples that retain the reference's temporal organization. Across 12 unseen target datasets, MarkovTS outperforms strong baselines in most distributional comparisons and generates diverse, reference-consistent sequences. As downstream augmentation, its samples yield overall gains across forecasting, classification, and anomaly detection benchmarks and diverse model families. Our code is available at https://github.com/blisky-li/MarkovTS.

Figures & tables

Figure 1: Generation settings and representation units. (a) In-domain training versus single-reference generation with frozen MarkovTS. (b) Series-, point-, and patch-level units versus the proposed multiscale state-transition representation.

Figure 2: Overview of MarkovTS. Left: multiscale state–transition representation learning. Middle: conditional flow pretraining. Right: single-reference zero-shot generation.

Metric	Dataset	MarkovTS	Winformer	ImagenFew	TimeDP	Diffusion-TS	TimeGAN	GT-GAN	TimeVAE	TimeVQVAE	TimeVQVAE-C
Maximum Mean Discrepancy	Electricity	0.001 $\pm$ 0.001	0.001 $\pm$ 0.002	0.002 $\pm$ 0.003	0.001 $\pm$ 0.001	0.003 $\pm$ 0.002	0.367 $\pm$ 0.255	0.254 $\pm$ 0.166	0.577 $\pm$ 0.006	0.152 $\pm$ 0.024	0.002 $\pm$ 0.001
	Solar	0.033 $\pm$ 0.003	0.035 $\pm$ 0.004	0.039 $\pm$ 0.011	0.041 $\pm$ 0.011	0.050 $\pm$ 0.012	0.628 $\pm$ 0.053	0.578 $\pm$ 0.039	0.353 $\pm$ 0.014	0.437 $\pm$ 0.020	0.058 $\pm$ 0.005
	Wind	0.013 $\pm$ 0.009	0.034 $\pm$ 0.014	0.071 $\pm$ 0.050	0.025 $\pm$ 0.017	0.035 $\pm$ 0.006	0.213 $\pm$ 0.017	0.170 $\pm$ 0.040	0.170 $\pm$ 0.004	0.131 $\pm$ 0.014	0.018 $\pm$ 0.007
	Traffic	0.087 $\pm$ 0.002	0.071 $\pm$ 0.005	0.080 $\pm$ 0.009	0.083 $\pm$ 0.034	0.111 $\pm$ 0.031	0.567 $\pm$ 0.057	0.538 $\pm$ 0.078	0.218 $\pm$ 0.007	0.213 $\pm$ 0.016	0.089 $\pm$ 0.001
	Taxi	0.110 $\pm$ 0.008	0.085 $\pm$ 0.010	0.108 $\pm$ 0.042	0.095 $\pm$ 0.023	0.131 $\pm$ 0.014	0.275 $\pm$ 0.054	0.319 $\pm$ 0.032	0.139 $\pm$ 0.007	0.128 $\pm$ 0.004	0.109 $\pm$ 0.014
	Pedestrian	0.032 $\pm$ 0.006	0.040 $\pm$ 0.008	0.041 $\pm$ 0.012	0.044 $\pm$ 0.020	0.071 $\pm$ 0.019	0.090 $\pm$ 0.030	0.112 $\pm$ 0.019	0.065 $\pm$ 0.002	0.067 $\pm$ 0.007	0.058 $\pm$ 0.002

Table 1: Time-series generation quality on non-overlapping length-168 windows from length-512 outputs conditioned on length-512 references. Lower is better; values are five-seed mean

\pm

sample standard deviation. Best and second-best methods are bold and underlined .

Metric	Elec.	Solar	Wind	Traffic	Taxi	Ped.	Air	Temp.	Rain	NN5	Fred-MD	Exchange	Mean
$\Delta$ Shape	0.016	0.017	0.093	0.056	0.041	0.127	0.074	0.036	0.040	0.018	0.032	0.057	0.051
$\Delta$ ACF	0.230	0.085	0.234	0.124	0.152	0.177	0.237	0.078	0.056	0.093	0.233	0.242	0.162
$\Delta$ PSD	0.250	0.122	0.242	0.160	0.214	0.218	0.300	0.148	0.220	0.113	0.171	0.236	0.199
Binary retrieval	95.5	95.7	93.8	98.8	99.4	92.0	95.8	92.3	96.7	75.9	92.2	96.0	93.7
100-way correct	58.9	51.6	71.2	84.1	89.1	45.8	86.6	45.1	78.3	26.0	46.3	77.3	63.4
100-way swapped	59.2	51.9	69.9	84.2	89.4	46.7	84.0	45.0	78.0	25.6	46.5	76.6	63.1

Table 2: Reference-specific fidelity under fixed-noise condition swaps. Entries are five-seed means; Appendix E.1.1 reports standard deviations.

Figure 3: Conditional distributions across ten held-out datasets. Panels show references, medians, and 50%/95% empirical intervals; inclusion rate denotes reference coverage by the 95% interval.

Variant	Metric	Elec.	Solar	Wind	Traffic	Taxi	Ped.	Air	Temp.	Rain	NN5	Fred-MD	Exchange
MarkovTS	MMD	0.001	0.032	0.019	0.087	0.101	0.032	0.009	0.142	0.031	0.180	0.002	0.124
	flat-KL	0.001	0.009	0.147	0.003	0.002	0.007	0.019	0.161	0.007	0.043	0.244	1.631
Random states	MMD	0.002	0.236	0.023	0.168	0.118	0.049	0.016	0.134	0.046	0.205	0.003	0.148
	flat-KL	0.059	0.689	0.189	0.144	0.075	0.088	0.039	0.134	0.010	0.106	0.364	5.030
Random transitions	MMD	0.002	0.190	0.023	0.130	0.119	0.054	0.017	0.152	0.053	0.231	0.002	0.147
	flat-KL	0.061	0.842	0.165	0.131	0.146	0.148	0.046	0.109	0.015	0.193	0.200	3.068

Table 3: Generation quality under state–transition code interventions and patch-based comparison.

Figure 4: State–transition complementarity on Solar at span 32. (a) Real patch pairs sharing state IDs but assigned distinct transition codes. (b) Occurrence centroids and covariance ellipses. (c) Scale-level within-code dispersion reduction against count-preserving permutations across datasets; gray points are dataset medians, and magenta diamonds are macro-medians with 95% bootstrap CIs.

Backbone	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	Imp.
	ECL		ETTh1		ETTh2		Exchange		Traffic		Weather
CATS	.258/ .245	.165/ .161	.443/ .423	.448/ .425	.425/ .384	.392/ .355	.420/.421	.388/ .387	.284/ .252	.421/ .402	.258/ .249	.221/.225	10/12
iTrans.	.259/.261	.164/.169	.473/ .433	.485/ .421	.439/ .427	.421/ .409	.478/ .447	.464/ .419	.289/.297	.412/.429	.267/ .258	.233/ .230	8/12
SparseTSF	.265/ .261	.173/ .171	.429/ .417	.427/ .412	.427/ .414	.399/ .389	.481/ .425	.478/ .390	.295/ .279	.445/.458	.283/ .276	.252/.255	10/12
TQNet	.246/.247	.158/.158	.425/.428	.422/.429	.417/ .416	.391/.393	.454/ .427	.428/ .387	.265/ .259	.410/ .398	.249/.252	.222/.223	5/12
OLinear	.298/ .297	.188/ .186	.428/.429	.414/.415	.416/ .412	.389/ .386	.456/ .439	.435/ .402	.328/ .321	.465/ .453	.250/.254	.221/.223	8/12

Table 4: Forecasting performance averaged over four horizons. Cells show Real only / Real + MarkovTS ; improvements are bold. Imp. counts improved dataset–metric pairs out of 12.

Classifier	Acc. $\uparrow$	BAcc. $\uparrow$	F1 $\uparrow$	AUROC $\uparrow$	LL $\downarrow$	Sens. $\uparrow$	Spec. $\uparrow$	Imp.
ResNet1D	68.15/ 68.94	67.94/ 68.86	65.05/ 67.12	83.71/ 85.05	1.13/ 1.07	66.02/ 69.33	69.95/69.21	6/7
TimesNet	65.84/ 68.36	65.03/ 66.94	63.86/ 65.26	83.32/ 84.13	1.16/ 1.10	66.28/ 66.73	65.03/ 68.30	7/7
ConvTran	69.31/ 70.23	68.01/ 69.16	67.93/67.49	85.52/ 85.65	0.82/ 0.79	70.49/69.10	67.36/ 70.65	5/7
Arsenal	73.21/73.17	71.34/71.32	71.16/ 71.31	84.39/ 84.85	5.56/ 5.12	71.19/ 71.53	74.17/73.77	4/7

Table 5: Classification on 23 UEA datasets: Real only / Real + MarkovTS . Bold: improvements; Imp.: improved metrics. Percentages except LL.

Detector	A-P $\uparrow$	A-R $\uparrow$	R-A-P $\uparrow$	R-A-R $\uparrow$	V-PR $\uparrow$	V-ROC $\uparrow$	Imp.
DLinear	.233/ .253	.672/ .679	.255/ .273	.713/ .715	.254/ .271	.710/ .714	6/6
TranAD	.278/.278	.674/ .676	.267/.261	.676/ .677	.264/.259	.673/ .675	3/6
CATCH	.248/ .254	.675/ .683	.278/ .284	.720/ .726	.275/ .281	.717/ .723	6/6
ModernTCN	.237/ .241	.660/ .664	.259/ .262	.704/ .708	.257/ .261	.702/ .705	6/6
TimesNet	.268/.267	.689/.685	.286/ .290	.731/.730	.285/ .289	.729/.727	2/6

Table 6: Anomaly-detection on 26 datasets. Cells show Real only / Real + MarkovTS ; improvements are bold. Higher is better; Imp. counts improved metrics. A-P/A-R: pointwise PR-/ROC-AUC; R-A-P/R-A-R: range-aware AUCs; V-PR/V-ROC: PR/ROC volumes under surface.

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$\mathcal{D}_{\mathrm{pre}},\mathcal{Q}_{\mathrm{pre}}$	Pretraining corpus and its set of source-domain distributions.
$q_{},R_{},T_{*}$	Unseen target distribution, evaluation reference pool, and disjoint target test set. Each generated sample uses one member of $R_{*}$ .
$X_{\mathrm{ref}},K_{\mathrm{eval}}$	Inference reference and number of references used in repeated single-reference evaluation.
$X\in\mathbb{R}^{D\times L}$	A length- $L$ time series comprising $D$ aligned variable sequences, each modeled independently.
$\bar{X},P,n_{h}$	Standardized input, canonical patch dimension, and number of padded intervals at scale $h$ .
$\mathcal{H},H,h$	Set, number, and index of temporal scales.

Appendix

Table 7: Notation for the MarkovTS formulation, representation, and generator.

Stage	Objective	Weight
State	Normalized-shape reconstruction	1.00
	Code commitment	1.00
	Query isotropy	0.10
	Perturbation consistency	0.05
	Delayed negative separation	$0.02\rho_{S}(s)$
Transition	Full-resolution reconstruction	1.00

Appendix

Table 8: Objective weights used in state warm-up and transition learning. The negative-separation weight follows the ramp

\rho_{S}(s)

Stage	Updates	Learning rate	LR warm-up	Effective batch
State warm-up	20,000	$10^{-4}$	200	84 ( $4\times 21$ )
State–transition	160,000	$10^{-4}$	1,600	84 ( $4\times 21$ )
Flow, final phase	2,400	$10^{-5}$	100	10,240 ( $8\times 1280$ )

Appendix

Table 9: Pretraining settings by stage. All stages use AdamW, bfloat16, and gradient clipping at norm 1.

Representation configuration
Component	Configuration
Base patch / temporal spans	$16$ / $\{16,32,64,128,256\}$
State codebook	$K_{S}=1024$ , dimension $64$ , EMA $0.99$
Transition codebook	$K_{T}=1024$ , dimension $64$ , EMA $0.99$
Conditional flow: final optimization phase
Flow backbone	width $288$ , depth $8$ , heads $8$ , MLP ratio $4$

Appendix

Table 10: Representation and conditional flow configurations used by MarkovTS.

Length	Batch/GPU	Flow-only	End-to-end
512	128	323.02	128.89
1024	96	221.13	74.40
2048	64	166.73	43.75

Appendix

Table 11: Generation throughput aggregated across four RTX 4090 24GB GPUs. Rates count complete sequences per second; batch sizes are per GPU.

Dataset	Application	Frequency	Scale	Content and temporal extent
Electricity	Energy	Hourly	321 clients	Electricity consumption, 2012–2014
Solar	Energy	Hourly	137 series	Solar power production in Alabama, 2006
Wind	Energy	4 seconds	1 long series	AEMO wind production, beginning August 2019
Traffic	Transportation	10 minutes	963 sensors	Freeway-lane occupancy in the San Francisco Bay Area over 440 days
Taxi	Transportation	30 minutes	1,214 locations	New York City taxi rides in January 2015 and January 2016
Pedestrian	Transportation	Hourly	66 sensors	Pedestrian counts in Melbourne, May 2009–April 2020

Appendix

Table 12: Held-out datasets for generation evaluation.

Dataset	Application	Frequency	Ch.	Mean length	Training values	Split
ECL	Energy	Hourly	321	18,412	5,910,252	7:1:2
ETTh1	Energy	Hourly	7	8,640	60,480	6:2:2
ETTh2	Energy	Hourly	7	8,640	60,480	6:2:2
Exchange	Economy	Daily	8	5,311	42,488	7:1:2
Traffic	Transportation	Hourly	862	12,280	10,585,360	7:1:2
Weather	Environment	10 minutes	21	36,887	774,627	7:1:2

Appendix

Table 13: Forecasting datasets and chronological splits. Mean length counts training time steps; training values count scalar observations.

Dataset	Train	Test	Ch.	Mean length	Training values	Cls.	Type
ArticularyWordRecognition	275	300	9	144	356,400	25	Motion
AtrialFibrillation	15	15	2	640	19,200	3	Biosignal
CharacterTrajectories	1422	1436	3	119 (60–182)	507,654	20	Motion
Cricket	108	72	6	1,197	775,656	12	Motion
DuckDuckGeese	50	50	1345	270	18,157,500	5	Audio
ERing	30	270	4	65	7,800	6	Motion

Appendix

Table 15: Classification datasets used for downstream evaluation.

Model	Optimizer / learning rate	Batch size	Maximum epochs
ResNet1D	Adam / $10^{-3}$	64	100
TimesNet	RAdam / $10^{-3}$	16	30
ConvTran	RAdam / $10^{-3}$	16	100
Arsenal	25 members; 2,000 kernels each	—	—

Appendix

Table 16: Classification training configurations.

Dataset	Series	Mean length	Ch.	Training values
ASD	12	8,527.6	19	1,944,289
CalIt2	1	2,520.0	2	5,040
CATSv2	4	28,471.8	17	1,936,079
CICIDS	1	85,115.0	72	6,128,280
Creditcard	1	142,403.0	29	4,129,687
DAPHNET	7	29,241.0	9	1,842,183

Appendix

Table 17: Anomaly-detection dataset statistics for the original training segments.

Model	Window	Optimizer / learning rate	Batch size	Maximum epochs
DLinear	100	Adam / $10^{-4}$	64	10
TranAD	100	Adam / $10^{-4}$	64	5
CATCH	96	Adam / $10^{-4}$ , $10^{-5}$	64	3
ModernTCN	100	Adam / $10^{-3}$	64	1
TimesNet	100	Adam / $10^{-4}$	32	10

Appendix

Table 18: Anomaly-detection training configurations. CATCH uses separate optimizers for its main and mask networks.

Dataset	ImagenFew	MarkovTS
Electricity	0.5226	0.3845
Solar	0.1857	0.4350
Wind	2.3173	0.6314
Traffic	0.6135	0.6471
Taxi	0.6176	0.4889
Pedestrian	0.4465	2.2981

Appendix

Table 19: TS2Vec-based Context-FID at sequence length 168. Lower is better; bold marks the better method on each dataset.

Dataset	$\Delta$ Shape-TS2Vec	$\Delta$ ACF	$\Delta$ PSD	Binary (%)	100-way correct/swapped (%)
Electricity	$0.0157\pm 0.0017$	$0.2299\pm 0.0195$	$0.2500\pm 0.0243$	$95.5\pm 1.1$	$58.9\pm 3.8$ / $59.2\pm 4.3$
Solar	$0.0165\pm 0.0025$	$0.0852\pm 0.0120$	$0.1218\pm 0.0102$	$95.7\pm 1.1$	$51.6\pm 2.7$ / $51.9\pm 2.9$
Wind	$0.0934\pm 0.0034$	$0.2341\pm 0.0109$	$0.2424\pm 0.0095$	$93.8\pm 0.8$	$71.2\pm 1.6$ / $69.9\pm 2.1$
Traffic	$0.0559\pm 0.0005$	$0.1235\pm 0.0107$	$0.1595\pm 0.0116$	$98.8\pm 0.3$	$84.1\pm 0.7$ / $84.2\pm 1.2$
Taxi	$0.0414\pm 0.0016$	$0.1523\pm 0.0063$	$0.2138\pm 0.0058$	$99.4\pm 0.2$	$89.1\pm 0.8$ / $89.4\pm 0.9$
Pedestrian	$0.1271\pm 0.0167$	$0.1774\pm 0.0073$	$0.2178\pm 0.0066$	$92.0\pm 1.4$	$45.8\pm 1.1$ / $46.7\pm 1.7$

Appendix

Table 20: Fixed-noise reference-swap analysis. Distance columns are swapped-minus-correct distances to the original reference; positive values indicate that changing only the condition moves the output away from its original owner. Retrieval targets the active condition. Values are five-seed mean

\pm

sample standard deviation; chance is 50% for binary and 1% for 100-way retrieval.

Dataset	Replication	$\sigma=0.05$	$\sigma=0.1$	$\sigma=0.2$	$\sigma=0.5$	$\sigma=1$	MarkovTS
MMD $\downarrow$
Electricity	0.001 $\pm$ 0.001	0.001 $\pm$ 0.001	0.001 $\pm$ 0.002	0.001 $\pm$ 0.001	0.001 $\pm$ 0.002	0.002 $\pm$ 0.002	0.001 $\pm$ 0.001
Solar	0.035 $\pm$ 0.005	0.037 $\pm$ 0.005	0.038 $\pm$ 0.006	0.040 $\pm$ 0.006	0.049 $\pm$ 0.009	0.193 $\pm$ 0.011	0.033 $\pm$ 0.003
Wind	0.026 $\pm$ 0.015	0.028 $\pm$ 0.020	0.024 $\pm$ 0.018	0.023 $\pm$ 0.016	0.022 $\pm$ 0.007	0.021 $\pm$ 0.005	0.013 $\pm$ 0.009
Traffic	0.070 $\pm$ 0.006	0.092 $\pm$ 0.003	0.092 $\pm$ 0.003	0.092 $\pm$ 0.003	0.098 $\pm$ 0.004	0.165 $\pm$ 0.009	0.087 $\pm$ 0.002
Taxi	0.094 $\pm$ 0.011	0.099 $\pm$ 0.000	0.099 $\pm$ 0.000	0.098 $\pm$ 0.000	0.093 $\pm$ 0.000	0.106 $\pm$ 0.000	0.110 $\pm$ 0.008

Appendix

Table 21: Generation versus reference replication and Gaussian perturbation. Values are five-seed mean

\pm

standard deviation; lower is better. Bold marks the best means at displayed precision.

			Random			Stochastic
Dataset	Metric	MarkovTS	States	Transitions	Both	States	Transitions	Both	Patch- Flow
Elec.	MMD	0.001 $\pm$ 0.000	0.002 $\pm$ 0.002	0.002 $\pm$ 0.002	0.003 $\pm$ 0.002	0.001 $\pm$ 0.001	0.002 $\pm$ 0.002	0.002 $\pm$ 0.002	0.003 $\pm$ 0.002
	flat-KL	0.001 $\pm$ 0.000	0.059 $\pm$ 0.044	0.061 $\pm$ 0.041	0.068 $\pm$ 0.039	0.005 $\pm$ 0.003	0.012 $\pm$ 0.008	0.015 $\pm$ 0.013	0.054 $\pm$ 0.031
Solar	MMD	0.032 $\pm$ 0.003	0.236 $\pm$ 0.008	0.190 $\pm$ 0.011	0.516 $\pm$ 0.008	0.034 $\pm$ 0.004	0.034 $\pm$ 0.003	0.034 $\pm$ 0.003	0.045 $\pm$ 0.006
	flat-KL	0.009 $\pm$ 0.000	0.689 $\pm$ 0.036	0.842 $\pm$ 0.027	1.099 $\pm$ 0.046	0.015 $\pm$ 0.008	0.014 $\pm$ 0.007	0.020 $\pm$ 0.010	0.173 $\pm$ 0.018
Wind	MMD	0.019 $\pm$ 0.001	0.023 $\pm$ 0.026	0.023 $\pm$ 0.025	0.023 $\pm$ 0.026	0.023 $\pm$ 0.026	0.023 $\pm$ 0.026	0.023 $\pm$ 0.026	0.033 $\pm$ 0.030

Appendix

Table 22: Generation quality under code interventions and patch-based comparison. Values are five-seed mean

\pm

sample standard deviation. Lower is better.

Metric	Dataset	512	1024	2048
MMD	Electricity	$0.001\pm 0.001$	$0.002\pm 0.001$	$0.002\pm 0.001$
	Solar	$0.033\pm 0.003$	$0.038\pm 0.005$	$0.036\pm 0.007$
	Wind	$0.013\pm 0.009$	$0.017\pm 0.013$	$0.021\pm 0.017$
	Traffic	$0.087\pm 0.002$	$0.222\pm 0.022$	$0.194\pm 0.011$
	Taxi	$0.110\pm 0.008$	$0.102\pm 0.003$	$0.098\pm 0.001$
	Pedestrian	$0.032\pm 0.006$	$0.037\pm 0.005$	$0.036\pm 0.006$

Appendix

Table 23: Generation quality across reference and output lengths. Lower is better; values are five-seed mean

\pm

sample standard deviation. All outputs are evaluated through fixed, non-overlapping length-168 windows.

Figure 5: Representative state and transition codes at temporal span 16. (a) Assigned normalized patches and their mean. (b) Mean previous/current patches and one-standard-deviation bands. $n$ and $d$ denote the number of assignments and represented datasets, respectively.

Figure 6: Transition-code examples within fixed state pairs on Electricity, Solar, Wind, Traffic, Taxi, and Pedestrian. Each panel shows three real patch-pair medoids.

C

denotes temporal scale,

S

the ordered state pair,

T

the transition code, and

n

its occurrence count. Annotations report changes in level, log-amplitude, and slope.

Figure 7: Transition-code examples within fixed state pairs on Air, Temperature, Rain, NN5, Fred-MD, and Exchange, using the notation of Figure 6 . The dagger marks Fred-MD’s lower-support qualitative example.

Figure 8: Coarse-to-fine conditioning ablation with a shared Gaussian source. Columns progressively remove the coarsest condition;

\Delta

is the standardized RMS distance from the full five-scale output.

Figure 9: Distributional diagnostics on four held-out datasets. Columns compare value density, autocorrelation, and normalized power spectrum for real validation data (black) and MarkovTS samples (blue).

Figure 10: Intermediate states along a conditional flow path. The final panel compares the reference with the generated realization.

		CATS			iTransformer			SparseTSF			TQNet			OLinear
Dataset	$H$	R	R+M	O	R	R+M	O	R	R+M	O	R	R+M	O	R	R+M	O
MAE $\downarrow$
ECL	96	.232	.217	.223	.230	.233	.235	.244	.237	.238	.220	.218	.221	.274	.273	.274
	192	.250	.233	.239	.252	.248	.252	.252	.248	.249	.239	.237	.240	.287	.288	.289
	336	.260	.250	.256	.264	.264	.268	.266	.264	.264	.248	.252	.256	.301	.303	.304
	720	.291	.281	.290	.289	.299	.302	.297	.295	.296	.277	.280	.287	.329	.323	.338

Appendix

Table 24: Forecasting MAE and MSE by horizon (lower is better). R: Real only; R+M: Real + MarkovTS; O: Online. Imp.: relative error reduction (%) from R.

Dataset	Acc. $\uparrow$	BAcc. $\uparrow$	F1 $\uparrow$	AUROC $\uparrow$	LL $\downarrow$	Sens. $\uparrow$
ResNet1D
ArticularyWordRecognition	95.78/88.78	95.78/88.78	95.78/87.48	99.94/99.71	0.16/0.42	= Acc.
AtrialFibrillation	11.11/13.33	11.11/13.33	8.85/10.73	37.56/40.22	4.18/4.13	= Acc.
CharacterTrajectories	98.84/99.28	98.75/99.21	98.84/99.28	99.98/99.99	0.05/0.03	= Acc.
Cricket	98.15/98.15	98.15/98.15	98.14/98.14	99.97/99.99	0.06/0.04	= Acc.
DuckDuckGeese	56.67/55.33	56.67/55.33	55.66/56.01	82.37/81.68	1.62/2.17	= Acc.

Appendix

Table 25: Per-dataset classification: Real only/Real + MarkovTS. Arrows indicate better performance. For multiclass datasets, = Acc. denotes Sens. and Spec. equal to Acc. under the benchmark convention.

Dataset	A-P $\uparrow$	A-R $\uparrow$	R-A-P $\uparrow$	R-A-R $\uparrow$	V-PR $\uparrow$	V-ROC $\uparrow$
DLinear
ASD	0.179/0.172	0.762/0.762	0.208/0.204	0.815/0.814	0.205/0.200	0.806/0.806
CATSv2	0.064/0.063	0.567/0.564	0.078/0.077	0.654/0.650	0.079/0.078	0.648/0.645
CICIDS	0.002/0.002	0.748/0.749	0.002/0.002	0.683/0.680	0.002/0.002	0.699/0.700
CalIt2	0.100/0.108	0.776/0.800	0.101/0.107	0.808/0.826	0.099/0.105	0.799/0.818
Creditcard	0.070/0.055	0.919/0.748	0.036/0.006	0.847/0.589	0.035/0.010	0.851/0.622

Appendix

Table 26: Per-dataset anomaly detection: Real only/Real + MarkovTS. Higher is better.

Figure 11: Generation under partial code randomization on Electricity, Solar, Wind, and Traffic. Rows randomize states, transitions, or both; columns show replacement fractions. Colored curves are generated sequences; dashed gray curves are references.

Figure 12: Generation under partial code randomization on Taxi, Pedestrian, Air (KDDCup), and Temperature.

Figure 13: Generation under partial code randomization on Rain, NN5, Fred-MD, and Exchange.

Time Series Generation

Time series generation creates synthetic sequential data that preserve temporal patterns, cross-variable structure, and controllable conditions.

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UPLOTS: A Unified Pretrained Language Model for Constrained Time-series Generation

In time-series generation, existing approaches typically handcraft ortrain a separate model for each dataset, which hinders their scalability and fails to leverage shared temporal structures across domains. To address this fragmentation, we propose UPLOTS, a Unified, Prompt-guided Language model framework fOr constrained Time-Series Generation across diverse domains. Instead of building task-specific models, UPLOTS leverages a single pre-trained transformer backbone guided by learned constraint prompts, enabling on-demand generation with precise pattern control. One key innovation is our dynamic multi-dataset loss re-weighting and prompt-to-pattern mapping, which allows UPLOTS to internalize diverse temporal structures during training and conditionally generate them at inference. We evaluate UPLOTS on four real-world benchmarks and multiple constraint settings, including peak-period, calendar, load-level, and volatility patterns. Additional held-out constraint-combination and downstream forecasting experiments further demonstrate that UPLOTS generalizes beyond the original peak-pattern setting and improves data augmentation under scarce real-data regimes. Our code and baselines are available at github repo: https://github.com/cruiseresearchgroup/UPLOTS.

Du Yin, Hao Xue, Jinliang Deng +4

University of New South Wales Sydney, NSW, Australia · HKUST(GZ) China · BUAA Beijing, China

Constrained Generative Modeling Time Series Generation Time Series Data Augmentation Conditional Generative Modeling Time-Series Foundation Models

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Jun 13, 2026

Towards a Unified Generative Model for Scarce Time Series with Domain Experts

Synthesizing realistic time series with generative models has wide-ranging applications in real-world scenarios. Despite recent progress, most existing methods are trained under the assumption of abundant training data, which substantially limits their effectiveness in data-scarce settings. In this paper, we propose TimeMoDE, a novel framework that integrates Diffusion Transformers with Mixture-of-Experts to exploit both domain adaptability and diffusion-stage awareness for time series generation under data scarcity. It is pre-trained on a large-scale collection of multi-domain datasets to extract domain-agnostic temporal representations and domain-specific information benefiting generalization during fine-tuning. We propose Domain Prompts to condition expert assignment for indistinguishable noised tokens, mitigating the limitations of capturing inter-dataset relationships. Moreover, we incorporate diffusion timestep signals to equip the experts with awareness of time series degradation variations, facilitating adaptive calibrate to stage-dependent denoising requirements. Extensive experiments demonstrate that TimeMoDE outperforms existing methods under diverse low-data settings. It establishes an innovative paradigm for advanced time series few-shot generation.

Zihao Yao, Qi Zheng, Jiankai Zuo +1

The Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, China.

Diffusion Transformer Time Series Generation Mixture-of-Experts Models Conditional Generative Modeling

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Nov 3, 2026

UniFlow: Unified Multi-Scale Flow Matching for Time Series Generation

Real-world time series exhibit complex dynamics across multiple temporal resolutions, yet effectively incorporating multi-scale information into generative modeling remains challenging without increasing generative complexity. We propose UniFlow, a unified framework that integrates multi-scale representation learning with efficient non-autoregressive generation through a shared-semantic discrete interface. Specifically, a multi-scale tokenizer employs shared-index voting to consolidate complementary temporal information into a single public-ID sequence, while scale-specific codebooks preserve the information required for reconstruction. Building on this unified representation, we develop geometry-aware categorical flow matching, which initializes transport from learned low-rank anchors and generates public identities non-autoregressively. This design captures multi-scale temporal structure without requiring multiple generative token streams or sequential token decoding. Experiments across four benchmarks and both short- and long-term settings demonstrate improved generative fidelity, strong cross-scale consistency, and substantial inference speedups over representative autoregressive and diffusion-based baselines. Code is available at https://github.com/William-Liwei/uniflow

Shibo Feng, Wei Li, Min Wu +2

College of Computing and Data Science, Nanyang Technological University, Singapore. · Shanghai Jiao Tong University and Beijing Zhongguancun Academy, Shanghai, China. · Institute for Infocomm Research and AIMfg, A* STAR, Singapore 138634. +1

Time Series Generation Flow-Based Generative Modeling Flow Matching Discrete Flow Matching

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Abstract

Time Series Generation

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