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

Shibo Feng; Wei Li; Min Wu; Chunyan Miao; Peilin Zhao

stat.MLNov 3, 2026

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

Authors: Shibo Feng, Wei Li, Min Wu, Chunyan Miao, Peilin Zhao

Organizations: 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. · School of Artificial Intelligence, Shanghai Jiao Tong University, Shanghai, China.

Abstract

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

Figures & tables

Fig. 1 : Overview of UniFlow. Stage 1 integrates aligned temporal representations through shared-index voting, yielding a single public-ID sequence and scale-specific codebooks. Stage 2 generates public identities using anchor-initialized categorical flow matching, followed by scale-specific embedding retrieval and decoding. Dashed blue and solid orange arrows denote training and sampling, respectively.

Dataset	Shared Ref. Token	Shared Ref. Seq	Scale-1 Token	Scale-1 Seq	Scale-2 Token	Scale-2 Seq
Sine	1.0000	1.0000	0.7873	0.2396	0.8540	0.3906
Stock	1.0000	1.0000	0.8053	0.3372	0.9053	0.5789
ETTh	1.0000	1.0000	0.8305	0.3389	0.8676	0.4281
Energy	1.0000	1.0000	0.8847	0.4974	0.8823	0.4868

TABLE I: Agreement with the canonical public-ID sequence. Shared Ref. denotes the full shared mapping, while Scale 1 and Scale 2 recover the public IDs from a single temporal view.

Category	Method	Sine			Stock			ETTh			Energy
Category	Method	DS $\downarrow$	PS $\downarrow$	C-FID $\downarrow$	DS $\downarrow$	PS $\downarrow$	C-FID $\downarrow$	DS $\downarrow$	PS $\downarrow$	C-FID $\downarrow$	DS $\downarrow$	PS $\downarrow$	C-FID $\downarrow$
GAN-based	TimeGAN	.011 $\pm$ .008	.093 $\pm$ .019	.101 $\pm$ .014	.102 $\pm$ .021	.038 $\pm$ .001	.103 $\pm$ .013	.114 $\pm$ .055	.124 $\pm$ .001	.300 $\pm$ .013	.236 $\pm$ .012	.273 $\pm$ .004	.767 $\pm$ .103
GAN-based	COT-GAN	.254 $\pm$ .137	.100 $\pm$ .000	1.337 $\pm$ .068	.230 $\pm$ .016	.047 $\pm$ .001	.408 $\pm$ .086	.325 $\pm$ .099	.129 $\pm$ .000	.980 $\pm$ .071	.498 $\pm$ .002	.259 $\pm$ .000	1.039 $\pm$ .028
VAE-based	TimeVAE	.041 $\pm$ .044	.093 $\pm$ .000	.307 $\pm$ .060	.145 $\pm$ .120	.039 $\pm$ .000	.215 $\pm$ .035	.209 $\pm$ .058	.126 $\pm$ .004	.805 $\pm$ .186	.499 $\pm$ .000	.292 $\pm$ .000	1.631 $\pm$ .142
Diffusion-based	DiffWave	.017 $\pm$ .008	.093 $\pm$ .000	.014 $\pm$ .002	.232 $\pm$ .061	.047 $\pm$ .000	.232 $\pm$ .032	.190 $\pm$ .008	.130 $\pm$ .001	.873 $\pm$ .061	.493 $\pm$ .004	.251 $\pm$ .000	1.031 $\pm$ .131
	DiffTime	.013 $\pm$ .006	.093 $\pm$ .000	.006 $\pm$ .001	.097 $\pm$ .016	.038 $\pm$ .001	.236 $\pm$ .074	.100 $\pm$ .007	.121 $\pm$ .004	.299 $\pm$ .044	.445 $\pm$ .004	.252 $\pm$ .000	.279 $\pm$ .045

TABLE II: Unconditional generation results on standard benchmarks (

\ell=24

). Best results in bold , second best underlined . Lower is better for all metrics. Original denotes the real-data PS reference. Results show mean

\pm

std over 5 runs.

$\ell$	Branch Dims	Branch Depths	Patch Sizes	Shared Weights	$K$	$d_{c}$	$s$
24	$192/320$	$2/4$	$2/4$	$0.4/0.6$	512	512	4
64	$192/320$	$2/4$	$2/4$	$0.4/0.6$	512	512	4
128	$192/320$	$2/4$	$2/4$	$0.4/0.6$	512	512	4
256	$192/320$	$2/4$	$2/4$	$0.4/0.6$	512	512	4

TABLE III: Stage 1 tokenizer settings used by UniFlow across sequence lengths.

$\ell$	Rank $r$	DiT Layers	$d_{\text{model}}$	Heads	ODE Steps	Bandwidth Factor
24	256	1	512	16	20	0.005
64	256–512	3	1024	16	20	0.005
128	512	3	1024	16	20	0.005
256	1024	3	1024	16	20	0.005

TABLE IV: Stage 2 generator settings used by UniFlow across sequence lengths.

	DS $\downarrow$			PS $\downarrow$			C-FID $\downarrow$
Method	$\ell=64$	$\ell=128$	$\ell=256$	$\ell=64$	$\ell=128$	$\ell=256$	$\ell=64$	$\ell=128$	$\ell=256$
ETTh Dataset
TimeGAN	.227 $\pm$ .078	.188 $\pm$ .074	.442 $\pm$ .056	.132 $\pm$ .008	.153 $\pm$ .014	.220 $\pm$ .008	1.130 $\pm$ .102	1.553 $\pm$ .169	5.872 $\pm$ .208
COT-GAN	.296 $\pm$ .348	.451 $\pm$ .080	.461 $\pm$ .010	.135 $\pm$ .003	.126 $\pm$ .001	.129 $\pm$ .000	3.008 $\pm$ .277	2.639 $\pm$ .427	4.075 $\pm$ .894
TimeVAE	.171 $\pm$ .142	.154 $\pm$ .087	.178 $\pm$ .076	.118 $\pm$ .004	.113 $\pm$ .005	.110 $\pm$ .027	.827 $\pm$ .146	1.062 $\pm$ .134	.826 $\pm$ .093
DiffWave	.254 $\pm$ .074	.274 $\pm$ .047	.304 $\pm$ .068	.133 $\pm$ .008	.129 $\pm$ .003	.132 $\pm$ .001	1.543 $\pm$ .153	2.354 $\pm$ .170	2.899 $\pm$ .289

TABLE V: Long-horizon generation on ETTh and Energy (

\ell=64,128,256

). Best and second-best results are bold and underlined ; all metrics are lower-better. Mean

\pm

std over 5 runs; Original is the real-data PS reference.

Method	Sine	Stock	ETTh	Energy
Diffusion-TS	9.57	10.12	11.85	34.92
SDformer-ar	0.15	0.18	0.40	0.15
MSDformer	0.95	0.96	0.30	0.96
UniFlow (Ours)	0.05	0.04	0.04	0.04
Speedup vs AR	3.0 $\times$	4.5 $\times$	7.5 $\times$	3.8 $\times$

TABLE VI: Inference time (seconds) for generating 1,024 samples at

\ell=24

. The comparison is calculated relative to the fastest autoregressive baseline on each dataset.

Dataset	Variant	DS / C-FID $\downarrow$	MAE / MSE $\downarrow$	Cycle Agree. $\uparrow$
Sine	Real (ref.)	–	–	0.665
	Shared gen.	0.003 / 0.0004	0.1201 / 0.0268	0.766
	Scale-1 gen.	0.008 / 0.009	0.1062 / 0.0208	0.499
	Scale-2 gen.	0.011 / 0.007	0.1110 / 0.0227	0.540
ETTh	Real (ref.)	–	–	0.711
	Shared gen.	0.003 / 0.001	0.1543 / 0.0428	0.768

TABLE VII: Single-view generation and tokenizer-cycle consistency. Cycle Agree. compares scale-specific IDs after decoding and re-encoding.

Dataset	Shared Dist.	S1 Dist.	S2 Dist.	S1/Shared	S2/Shared
Sine	0.455	15.185	13.908	33.3 $\times$	30.5 $\times$
ETTh	3.746	14.949	14.848	4.0 $\times$	4.0 $\times$
Energy	62.493	369.868	241.368	5.9 $\times$	3.9 $\times$

TABLE VIII: Coarse-view distributional fidelity under non-overlapping temporal aggregation

w\in\{2,4\}

. Distances are averaged across windows; lower is better. Ratios indicate the relative distances of single-scale variants to shared generation.

Condition	Initial Acc.	Refined Acc.	Correction	DS / C-FID
Scale-1 IDs	0.7873	0.9999	0.9996	0.0116 / 0.00024
Scale-2 IDs	0.8540	0.9999	0.9997	0.0109 / 0.00026

TABLE IX: Sine conditional public-ID refinement diagnostic. Initial accuracy is the token match between a single branch’s recovered IDs and the jointly voted shared IDs; refined accuracy is measured after the conditional Stage 2 refinement.

Dataset	MSE $\downarrow$					MAE $\downarrow$
Dataset	Shared	Scale-1	Scale-2	S1 $\Delta$	S2 $\Delta$	Shared	Scale-1	Scale-2	S1 $\Delta$	S2 $\Delta$
Sine	0.00004929	0.00005341	0.00006096	0.00000412	0.00001166	0.005348	0.005533	0.005819	0.000185	0.000471
Stock	0.00018091	0.00018585	0.00018173	0.00000495	0.00000082	0.008570	0.008625	0.008587	0.000055	0.000017
ETTh	0.00010566	0.00011746	0.00013094	0.00001180	0.00002528	0.007804	0.008116	0.008494	0.000312	0.000690
Energy	0.00005832	0.00008911	0.00016054	0.00003078	0.00010222	0.005546	0.005986	0.006699	0.000440	0.001153
Avg. $\Delta$	–	–	–	0.00001291	0.00003500	–	–	–	0.000248	0.000583

TABLE X: Reconstruction performance under shared and single-view public-ID assignments.

\Delta

denotes the increase in reconstruction error relative to the shared mapping. Lower values indicate better reconstruction quality.

Fig. 2 : t-SNE visualization of real and Stage 1 reconstructed samples under different public-ID assignments.

Fig. 3 : Multi-scale temporal structure under shared and single-scale generation. Top: Temporal aggregation gaps. Middle: Joint fine- and coarse-scale activity distributions. Bottom: Covariance ellipses of joint variation. Shared generation better preserves the real-data multi-scale structure.

Component	Variant	DS $\downarrow$	C-FID $\downarrow$
Tokenizer	Single-scale token flow	0.006	0.003
	Multi-scale, dilation-only	0.027	0.018
	Multi-scale, patch-based	0.003	0.001
Interface	Shared public IDs	0.003	0.001
	Scale-1 IDs only	0.345	0.363
	Scale-2 IDs only	0.316	0.326

TABLE XI: Ablation of multi-scale tokenization, shared-ID interface, and flow initialization on Energy.

Layer	Function	Description	Input Shape	Output Shape
1	Input permutation	Channel-first representation	$(B,\ell,d)$	$(B,d,\ell)$
2	Patch Conv1D	$d\to H$ , kernel/stride $p_{m}$	$(B,d,\ell)$	$(B,H,\ell_{m,0})$
3	ReLU	Activation	$(B,H,\ell_{m,0})$	$(B,H,\ell_{m,0})$
4	ResNet	Depth $n_{m}$ , dilation growth $g_{m}$	$(B,H,\ell_{m,0})$	$(B,H,\ell_{m,0})$
5	Downsampling + ResNet	Stride-2 Conv1D + ResNet, repeated $q_{m}$ times	$(B,H,\ell_{m,j-1})$	$(B,H,\ell_{m,j})$
6	Output Conv1D	$H\to d_{m}$ , kernel $3$	$(B,H,L)$	$(B,d_{m},L)$

TABLE XII: Detailed architecture of the Stage 1 multiscale encoders. Each branch employs scale-specific patching and residual modeling to produce aligned temporal representations of length

L

Layer	Function	Description	Input Shape	Output Shape
1	ReLU	Activation	$(B,H,L_{r})$	$(B,H,L_{r})$
2	Dilated Conv1D	$H\to H$ , kernel $3$ , dilation $\delta$ , padding $\delta$	$(B,H,L_{r})$	$(B,H,L_{r})$
3	ReLU	Activation	$(B,H,L_{r})$	$(B,H,L_{r})$
4	Pointwise Conv1D	$H\to H$ , kernel $1$	$(B,H,L_{r})$	$(B,H,L_{r})$
5	Residual connection	Output = Input + Conv output	$(B,H,L_{r})$	$(B,H,L_{r})$

TABLE XIII: Detailed architecture of the Stage 1 residual convolutional block, where

\delta

denotes the dilation rate and

L_{r}

the temporal feature length.

Layer	Function	Description	Input Shape	Output Shape
1	Shared-index voting	Weighted cosine similarity, vocabulary size $K$	$\{(B,d_{m},L)\}_{m=1}^{M}$	$(B,L)$
2	Codebook retrieval	Shared-ID lookup in scale-specific codebooks	$(B,L)$	$\{(B,L,d_{m})\}_{m=1}^{M}$
3	Feature fusion	Concatenate private embeddings, $d_{c}=\sum_{m}d_{m}$	$\{(B,L,d_{m})\}_{m=1}^{M}$	$(B,d_{c},L)$
4	Input Conv1D	$d_{c}\to H$ , kernel $3$	$(B,d_{c},L)$	$(B,H,L)$
5	ReLU	Activation	$(B,H,L)$	$(B,H,L)$
6	ResNet	Depth $n_{\mathrm{dec}}$ , reverse dilation	$(B,H,2^{j-1}L)$	$(B,H,2^{j-1}L)$

TABLE XIV: Detailed architecture of Stage 1 shared-ID assignment and reconstruction. Shared public IDs retrieve scale-specific codebook embeddings, which are fused for time-series reconstruction.

Layer	Function	Description	Input Shape	Output Shape
1	Low-rank anchor	Projection through $V\in\mathbb{R}^{r\times Ld_{c}}$	$(B,r)$	$(B,L,d_{c})$
2	Flow interpolation	$Z_{t}=(1-t)Z_{0}+tZ_{1}$	$Z_{0},Z_{1}:(B,L,d_{c})$	$(B,L,d_{c})$
3	Global token	Prepend one learned token	$(B,L,d_{c})$	$(B,L+1,d_{c})$
4	Input projection	Linear $d_{c}\to D$ + positional encoding	$(B,L+1,d_{c})$	$(B,L+1,D)$
5	Time embedding	Linear $1\to 4D$ + SiLU + Linear $4D\to 4D$	$(B,1)$	$(B,4D)$
6	DiT blocks	AdaLN + MHSA ( $A$ heads) + FFN ( $4D$ ), repeated $N_{f}$ times	$(B,L+1,D)$	$(B,L+1,D)$

TABLE XV: Detailed architecture of the Stage 2 non-autoregressive categorical flow generator. The DiT predicts categorical endpoint distributions for joint transport of all public-token positions.

Fig. 4 : t-SNE visualizations of the time series synthesized by UniFlow, SDformer and Diffusion-TS.

Fig. 5 : Kernel density estimation visualizations of the time series synthesized by UniFlow, SDformer and Diffusion-TS.

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Open paper AskPDF arXiv

Vector quantization (VQ) with autoregressive (AR) token modeling is a widely adopted and highly competitive paradigm for time-series generation. However, such models are fundamentally limited by exposure bias: during inference, errors can accumulate across sequential predictions, leading to pronounced quality degradation in long-horizon generation. To address this, we propose SDFlow (

\textbf{S}

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\textbf{D}

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Matching), a non-autoregressive framework that operates entirely in the frozen VQ latent space and enables parallel sequence generation via flow matching. We tackle three key challenges in making this transition: (1) eliminating exposure bias by replacing step-wise token prediction with a global transport map; (2) mitigating the high-dimensionality of VQ token spaces via a low-rank manifold decomposition with a learned anchor prior over the latent manifold; and (3) incorporating discrete supervision into continuous transport dynamics by introducing a categorical posterior over codebook indices within a variational flow-matching formulation. Extensive experiments show that SDFlow achieves state-of-the-art performance, improving Discriminative Score and substantially reducing Context-FID, particularly for challenging long-sequence generation. Moreover, SDFlow provides significant inference speedups over autoregressive baselines, offering both high fidelity and computational efficiency. Code is available at https://github.com/William-Liwei/SDFlow

Abstract

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