TARFVAE: Efficient One-Step Generative Time Series Forecasting via TARFLOW based VAE
Authors: Jiawen Wei
Lan Jiang
Pengbo Wei
Ziwen Ye
Teng Song
Chen Chen
Guangrui Ma
Venue: NeurIPS 2025 poster ()
Keywords: time series forecasting
generative model
normalizing flow
variational autoencoder
Primary area: deep_learning

Abstract: Time series data is ubiquitous, with forecasting applications spanning from finance to healthcare. Beyond popular deterministic methods, generative models are gaining attention due to advancements in areas like image synthesis and video generation, as well as their inherent ability to provide probabilistic predictions. However, existing generative approaches mostly involve recurrent generative operations or repeated denoising steps, making the prediction laborious, particularly for long-term forecasting. Most of them only conduct experiments for relatively short-term forecasting, with limited comparison to deterministic methods in long-term forecasting, leaving their practical advantages unclear. This paper presents TARFVAE, a novel generative framework that combines the Transformer-based autoregressive flow (TARFLOW) and variational autoencoder (VAE) for efficient one-step generative time series forecasting. Inspired by the rethinking that complex architectures for extracting time series representations might not be necessary, we add a flow module, TARFLOW, to VAE to promote spontaneous learning of latent variables that benefit predictions. TARFLOW enhances VAE's posterior estimation by breaking the Gaussian assumption, thereby enabling a more informative latent space. TARFVAE uses only the forward process of TARFLOW, avoiding autoregressive inverse operations and thus ensuring fast generation. During generation, it samples from the prior latent space and directly generates full-horizon forecasts via the VAE decoder. With simple MLP modules, TARFVAE achieves superior performance over state-of-the-art deterministic and generative models across different forecast horizons on benchmark datasets while maintaining efficient prediction speed, demonstrating its effectiveness as an efficient and powerful solution for generative time series forecasting. Our code is available at https://github.com/Gavine77/TARFVAE.

TARFVAE: Efficient One-Step Generative Time Series Forecasting via TARFLOW based VAE
Jiawen Wei
Lan Jiang
Pengho Wei
Meituan
Meituan
Meituan
Beijing, China wea.jiaawn@meittunncccm
Beijing, China
Beijing, China weipenggbo@meituan tuan.
jianglan09dmei tuan. com
Ziwen Ye Meituan
Teng Song
Chen Chen Mcituan
Meituan
Beijing, China
Beijing, China songteng020meitunn tuann..eeeuuut.mmmmmmm com
Beijing, China chenchen 1 10me tuan. com
Doziven@meituan.co com
Guangrui Ma"
Meituan
Beijing, China
magr@connect. ust.
Abstract
Time series data is ubiquitous, with forecasting applications spanning from fi- nance healthcare. Beyond popular deterministic methods, generative models are gaining attention due to adnnemments in areas like image synthesis and video gener- ation, as well as their inherent ability provide probabilistic predictions. However, existing generative approaches mostly involve recurrent generative operations or re- peated denoising steps, making the prediction laborious, particularly for long-term forecasting. Most of them only conduct experiments for relatively short-term fore- casting, with limited comparison to deterministic methods in long-term forecasting, leaving their practical advantages unclear. This paper presents TAREVAE, novel generative framework that combines the Transformer- (TARFLOW) and variational autoencoder (VAE) for efficient one-step generative time series forecasting. Inspired by the rethinking that complex architectures for extracting time series representations might not be necessary, we add flow module, TARFLOW, to VAE to promote spontancous Icarning of latent variables that bene- fit predictions. TARFLOW enhances VAE's posterior estimation by breaking the Gaussian assumption, thereby enabling a more informative latent space. TARFVAE only the forward process of TARFLOW, avoiding autoregressive inverse oper- ations and thus ensuring fast generation. During generation, it samples from the prior latent space and directly generates full-horizon forecasts via the VAE decoder. With simple MLP modules, TARFVAE achieves superior performance over state- of- of-the-art deterministic and generative models across different forecast horizons on benchmark datasets while maintaining efficient prediction speed, demonstrating its effectiveness as an efficient and powerful solution for generative time series forecasting, Our code is available at wttp:/hhtwbooom//aaaee////AAAAA
autoregressive flow
"Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
In various application fields such as transportation planning healthcare(21 and inventory management(3. long-term time series forecasting (LTSF) and uncertainty quantification are of vital importance. The former provides a solid basis for long-term decision-making by offering reliable prediction, while the latter delivers more comprehensive estimates, enabling robust decision- making through accounting for potential variability. Recently, deep learning has achieved remarkable success in these fields through capturing complex time series patterns[44g] and generating reliable uncertainty estimates [3
In the realm of long-term forecasting, various strategies have been proposed to enhance predictive performance. Most efforts have focused on Transformer-based models due to their proven capability in capturing long-term dependencies via attention mechanisms(6), Numerous studies aim to reduce the computational complexity of attention [648] and improve information extraction, while others apply vanilla Transformers mine intra-channel
inter-channel relationships [4 [ However, some studies 14, [5] argue that sophisticated designs might not necessary and suggest simple models could deliver results comparable to Transformer based models. This has spurred exploration into Linear- based or MLP-based methods that aim at more efficient utilization of historical information during training to improve prediction performance ( [6 17
Current LTSF methods are predominantly deterministic, producing point estimates without system- atically addressing uncertainty quantification. This oversight poses substantial risks to operational robustness, particularly given the intrinsic positive correlation between uncertainty magnitude and forecast horizon length. To achieve probabilistic forecasting, earlier models like DeepAR [1) employ recurrent neural networks (RNNs) to estimate parameters prespecified distributions (e.g., Gaussian) for each timestep. However, such methods impose restrictive parametric assumptions that may not capture complex temporal dynamics. Subsequent advancements have explored generative frameworks, including variational autoencoders (VAEs) [8 and diffusion models 10 [3), building upon their demonstrated success in adjacent domains 19) While diffusion models achieve state-of- ooffthe-art sample quality, their iterative denoising process incurs substantial computational overhead during inference. Recent attempts to accelerate generation 11
13 22 remain fundamentally constrained by the multi-step generation paradigm. By contrast, conventional 23 enables one-step generation by decoding samples from the prior latent space. However, many existing hybrid methods [24 introduce complex recurrent structures to capture temporal dependencies and generate predictions autoregressively, which undermine this computational advantage. Due to computational constraints, these generative models have primarily been developed and evaluated in short-term settings, raising concerns about their long-tems term efficacy and accuracy. Recently, Zhang et al. (27) systematically compared deterministic and probabilistic methods for long-term forecasting, whose results still highlight the need for models that can effectively address both point and probabilistic forecasting across diverse horizons.
Motivated by these considerations, we introduce TARFVAE, a novel VAE-based framework that strategically integrates two core objectives: (1) preserving the one-step generation capability of VAES to ensure computationally efficient inference, and (2) promoting spontaneous learning of latent variables that guarantee robust probabilistic forecasting performance. TARFVAE achieves these by simply incorporating a Transformer-basee autoregressive flow (TARFLOW) 28), which enables an enhanced posterior estimation. Note that the autoregressive inverse process of TARFLOW is not included so TARFVAE can perform one-step generation. Extensive experiments on eight real-world datasets demonstrate the superiority of TARFVAE over the existing state-of-the-ar deterministic and generative baselines.
2 Related Work
Long-term Time Series Forecasting Transformer-baat based models have achieved remarkable success in LTSF through their attention mechanisms, which effectively capture long-term dependenciesfé: B]. According to Qiu et al. (2]] these models can be categorized into channel-ing saannel-indeeendent and channel-dependent approaches. Initially, they aggregate channel information via linear mapping and use attention to extract temporal patterns. However, the high computational complexity of attention mechanisms poses challenges in long-term forecasting. To address this, significant efforts have focused on enhancing attention efficiency(6-5 30). Despite progress, channel-dependent

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strategies are more vulnerable to distributional shifts 14 31, channel-inden -ideeeededeeed approaches, which have shown superior performance 4 S PStchTSTT4 splits historical data into patches and applies a standard Transformer to model their correlations. Meanwhile, other studies have leveraged simple Linear-based or MI.P-based structures for time series modeling 14 [6 17 [3]. For instance, SOFTS[17] introduces an MLP--ased module to aggregate multiple channels and generate core representations for prediction.
prompting some researchers to explore For example,
Generative Models for LTSF To boost model robustness and reliability, recent studies have shifted from estimating the median distribution using generative models. Various generative models, such as VA [3 24), normalizing flows 32 33 and diffusion models(IO). have been applied this field. Transformer-MAF MMF the pioneering work in applying normalzing flows: it builds upon the Transformer architecture and utilizes Masked Autoregressive Flows (MAF) 34 for generating time series forecasts. Recently, diffusion models have gained prominence in LTSF because of their superior performance in adjacent domains 21). TimeGrad[OO) the first time series diffusion model, relied on an RNN to predict in an autoregressive manner, with the denoising process guided by hidden states generated by RNN. Instead of autoregressive decoding, CSDI[I] and SSSD[35] use self-supervised masking to guide the denoising process and make predictions. Methods like TimeDiff[33 and mrDiff (36 utilize different networks to incorporate historical information as conditions and employ conditional diffusion models for time series generation. However, diffusion-based models, though effective, require multiple steps to generate time series from noise, thus slowing inference. Unlike diffusion models, VAEs can efficiently generate data by directly decoding latent representations. Previous studies [8 26 improve the learning of latent space by better representing historical sequences through complex recurrent autoregressive operations, which compromise VAE's fast inference speed.
of time series capturing the complete time series
3 Preliminaries
3.1 Variational AutoEncoder
VAE 23 is an unsupervised generative model that models the input data distribution by learning a probabilistic latent space follows:
p(2) p(z[z) p(zlz)dz = (=)=)( p(2
p(z)
p(x)
p p(z)))p(z)dz== /(xx2)
(I)
where x is the input data and z is its latent representations. The prior p(=) is normally defined as a multivariate Gaussian distribution N(0, 7). The posterior p(2(x: can be arbitrary distribution and
VAE approximates it as (<2[z)) = ((((z), of) (x)). Thus VAE learns the problem by maximizing the log-likelihood of (
p(z)
log)(r)) = log E (e
p(x(2)
(2)
(2(xx)
p(z)
> Esng(= log p(x(=) ((=lxr)
(3)
log logp(x|>) - log (<([0)
= Eeng(ale)
(4)
p(2)
= -Zngg(=l)) [(<[))]]]]]]))) - K (L((())))l)(()
(5)
where 3 is the evidence lower bound (ELBO) of 2 accoring to Jensen's 's inequality. The first
term leads to reconstruct accurate x from z, and the second term minimizes the difference between the prior and approximated posterior to prompt the latent space to capture meaningful data representations. This enables VAE to generate new samples via p(=), x p(x(z).
VAE can be extended to conditional VAE by incorporating supervised labels The ELBO for log p(ry)) can be analogously derived follows:
g( ((=(<r,))
log p(xl)) 2 E [= logp(z|2.v) v) - log p(2ly)
(6)
E E [logp(>l y)] (L(((</2, v))ll:.))lpp(p)p)
(7)
where the prior, approximated posterior and reconstruction process are all conditioned on y.
3

---

3.2 Normalizing Flow
Normalizing flows 33 are invertible mappings f from R to R.. For X and
2 ~ 2, the density px (z) can be expressed by
0f(x), dx
(x(x)= - -22((())) det
(8)
Normalizing flows have the property that the inverse - (=) is easy to evaluate and computing the Jacobian determinant takes OD) time. Therefore, once the model is trained, a generative model is automatically obtained via 2 ~ Z, x = f (2). Real NVP designs an affine coupling layer to meet the above two conditions:
21 11
99)
22 (x2 ((x1)) @ exp(s(x11)
where can be randomly shuffled into two parts [+1 22]. and s(x1) and t(x1) are learnable functions whose outputs match the shape of æ2. The inverse of (9) is obvious and the Jacobian matrix of (9) is a lower triangular matrix. The determinant of the Jacobian is the product of the diagonal elements, so the log- iegddeterminat is
Oz Or
log det
Σ 81(11).
(10)
To achieve stronger nonlinearity, multiple coupling layers are composed together, creating chain of mappings: X' Zn + Zi + Zg ZK Z. The maximum likelihood estimation objective can then be written as
0zk
log (xg)x()) log
log det
(11)
0zk-1
Recently, Zhai et al. proposed TARFLOW 28 which could achieve more efficient nonlinear mappings. TARFLOW partitions x into more parts as [T1, 22 ..., In. and performs transformation following similar rule:
1 21
(2) = (z, - t (22z)) O exp(s
(12)
where j > 1 and æzj = [x1, .... I -.. The s(x<)) and t(zzz) are efficiently implemented by causal Transformer. Notably, the inverse of (12 becomes
F 21
(13)
xj bg O exp(- (E<s)) + (x2z)
where the inference of relies on Æejj making the inverse process autoregressive.
3.3
Time Series Forecasting
Time series forecasting uses historical time series E RC to predict the future values RC*H Here, represents the number of variables or channels, is the length of the lookback window, and H stands for the forecast horizon. C corresponds to multivariate time series; otherwise, it is termed univariate.
Deterministic methods perform point estimation via function as ÿ f(r),, whereas probabilistic methods model a distribution ((y|æ:) approximate the true p(ylæx).
TARFVAE
4.1 Overview
The architecture of TARFVAF, as illustrated in Figure builds upon a conditional VAE where input history æ conditions the generation of target series y. The Gaussian posterior assumption in Section

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3.1 fundamentally limits reconstruction accuracy in conventional VAEs, as Gaussian distributions constitute a tiny subset of all possible posterior distributions. To overcome this expressiveness limitation, we introduce TARFLOW to refine an initial Gaussian posterior {(=o|2r, y) into flexible complex distribution that closely matches the true posterior. Specifically, both and y are utilized for training, whereas only x: is used for inference.
first apply instance normalization 40 to remove the local statistics of the input history to stabilize the base prediction, and then restore them to the model prediction. Notably, during training, both æ and y are normalized based on z's 's mean and variance without using o's statistics. This ensures x normalization remains consistent between training and inference, regardless of y presence.
Instance normalization. Following many state-of-the-art models 4 5
39)
Series embedding. Then we perform series embedding 1 17 on the needed time series for the en- coder, decoder, prior and flow modules independently. Each module employs dedicated embedding layer to extract module-specific temporal patterns. This architectural isolation prevents cross-module interference while enabling targeted feature learning.
One-step generation. The prior and encoder modules parameterize two Gaussians, the prior p(=[æ) and initial posterior a ar, y), respectively. During training. the flow module transforms 2g q(20 x. y) to approximate 2 from the true posterior, while inference directly samples & ~ p(2|zr). Finally, the decoder maps to I conditioned on z, enabling efficient one-step full-horizon generation.
The training and inference process of TARFVAE can be formulated as follows:
Training
Apriors log prior = Prioo(Emll (x))
(14)
Mza log 0² = Encoder( Emb ([z, vi))
(15)
20 NH o200
(16)
TARFLOW (zo. Embs(((r,))
(17)
Decoder(2, Embs(x))
(18)
Inference
Mprior, , log 0² prior = Prior (Emb(x))
(19)
Eprior N (pprioor 2 )prorr)
(20)
0 Decoder Eprior, Emba(x))
(2pridrr
(21)
Below, we describe the TARFVAE implementation used in our work, while noting that alternative
approaches could be adopted.
training only
inference only
Pormutation
Input
Output
x
sufficient p(y
Encoder
(/20l2, 1/)
TARFLOW
g(=12.))
Charnel
Decodar
Prior
p(slz)
Time
Chamne
Figure 1: The overview of TARFVAE.
5

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4.2 MLP Foundation
Although many Transformer- based architectures such as PatchTST 4 iTranformer and DUET 39
have demonstrated that self attention can be effective for long-term forecasting, recent studies 14 15 argue that sophisticated designs might not be necessary and suggest simple models like feedforward neural networks could suffice for the job. To thoroughly test the TARFVAE, framework's s effectiveness and avoid confounding effects from elaborately designed temporal processing modules, we implement simple MLP blocks as shown in Figure 2 for basic input mixing, where the channel-wise mappings enable the capture of inter-channel dependencies. These MLP blocks form the architectural foundation across our encoder, decoder, and prior module.
Vers-caarowi MLP
Indendieeral KLP
Deloor
Figure 2: The MLP blocks.
In the prior module and encoder, following multiple MLP blocks, linear layers output the estimated mean and variance for the Gaussian prior p(z(z) and initial posterior ((20|<r, y) respectively as follows:
porior, log of oprior Linear (M LM (Emb) (x)))
(22)
Mag log o² Linearenc (M Blocks (Emby([a, (E (l))
(23)
The decoder aims to reconstruct using conditioned We chose augment via connecting full attention output where = queries out relevant information from æ. Subsequently, MLP blocks process this mixed information, and linear projection is used to achieve the final reconstruction of The process is outlined as follows:
Amiined = 2 - Full FullAttention( Embs(x) Embs(())
(24)
ÿ = Limear Blochssssee (Mmixedd)
(255)
4.3 TARFLOW
In the flow module, the input 20 and all intermediate latent variables {k .,, maintain consistent dimensionality RCXD where D represents the latent dimension. These variables are naturally partitioned by channels, and perform the transformation (12) conditioned ær y in each TARFLOW block as follows:
21 21
(26)
2j (z,- - ((x + Embs([a vi)) @ exp(s ((x Embs((x, <))))s))
Following the original implementation 28), we adopt dimension-reversing permutation between adjacent blocks. This module finally outputs zκ z.
Combining and (6), the training loss for single sample generation is derived as
Ozk
= - -Eng(=)Ea))
log logp(ulz,2) x) log g(50 1,
+
log det
+ log p(=
(27)
Ozk-
1=1
D
1
(n()
+
nnn y
Ino? z0.d
+ Ino p
2
km ol
(28)
1/ Myy
20
Pzz
2 Mpriio
+
2
0
2
20
2
o prior

---

where p(yl2,z) x) is chosen to be Guassian for continuous predictions and its mean My and variance of are implemented as ý and I in our work.
5
Experiments
5.1 Setup
Datasets. To comprehensively evaluate the performance of proposed TARFVAF, conduct extensive experiments on 8 widely-used real-world datasets: four ETT subsets (ETThl, ETTh2, ETTml. ETTm2), Electricity, Exchange, Weather 77. and Solar-Energy [4].
Baselines. We extensively choose the recent state-of-the-art models to serve as baselines. For MLP-based methods (SOFTS T6) TSMixer 9 and DLinear [4] and Transformer- based models (DUETT3), iTransformer PatchTST[44] Crossformer 30] and FEDformer(8) (8). For generative approaches, given their dis- tinct evaluation protocols compared to deterministic approaches, we follow mr- (36 and com- pare against both mr-Diff and its benchmarked generative baselines: TimeDiff[13], TimeGrad 10]
deterministic methods, include Linear-
CSDILT SSSD 35
D 22), CPF and PSA-GAN 43
Implementation details. When comparing with deterministic models, the long-term forecasting benchmarks follow the common setting ( (7), with the lookback window length L set to 96 and the prediction horizon H to (96, 192, 336, 720} for all datasets. For comparison with mr-Diff and its benchmarked baselines, we adopt the same configurations: H is 168 for Electricity and ETTh1, 192 for ETTml, and 672 for Weather, while L is chosen from {96, 192, 336, 720, 1440]. Mean Squared Error (MSE) and Mean Absolute Error (MAE) are adopted as evaluation metrics. Since we can sample different sizes of results once our model is trained, we calculate MSE and MAE for the median of sampled results. We also compute the Continuous Ranked Probability Score (CRPS) based on sampled results
probabilistic forecasting metric. All experiments are implemented using PyTorch[45 [45] on a single Nvidia-H20 GPU with 141 GB memory, except for the inference efficiency comparison experiment which is conducted an Nvidia-A6000 GPU with 48 GB memory to align with the experimental settings of the compared generative baselines. Our training process is guided by the loss function (28) and employs the ADAM optimizer, and the best model is selected based on the MSE of the median of 50 generated samples on the validation set.
5.2 Main results
Table D presents the multivariate time series forecasting performance of TARFVAE in contrast with selected deterministic baselines, where the results of sampling 200 are shown and the full results of different sample sizes can be seen in Table The results demonstrate that TARFVAE achieves the highest number of best outcomes across various forecast horizons in all 8 datasets. Notably, TARFVAE consistently achieves superior performance under varing forecast horizons in out of 8 datasets with significant improvements. For instance, it reduces average MSE by 4.3% on ETTh2 and 4.8% on Weather, respectively. These results not only demonstrate TARFVAE's precision advantages compared to state-of state-of-the of-the-art deterministic methods but also reveal its ability to produce robust performance considerable long- forg-term forecasting (e.g.. 720-horizon predictions).
Table shows the performance of TARFVAE compared to other generative methods. TARFVAE achieves the best overall performance, securing top-1 positions in 5 out of 10 metrics and ranking second metrics. To compare inference efficiency, we rerun TARFVAE under the same configu- rations the baselines, since some baselines such as mr-Diff and TimeDiff are The results shown in Table demonstrate TARFVAE'S significant speed ad advantages: for instance, it reduces inference time by 85.6% compared mr-Diff at horizon even more so when compared to other methods. Furthermore, TARFVAE maintains computational stability when handling extended forecasting horizons only the final linear layer's dimensionality increases, while other generative methods require progressive time increments. Additionally, its parallelized sampling computation ensures minimal latency variation (from to 200 samples) under moderate sampling scales. These findings collectively establish TARFVAE as both an accurate and efficient approach, enabling high-quality probabilistic forecasts through one-step generation while outperforming oa-t--oftthe-ar generative methods in computational scalability.
soureedu.
720 in the ETThl dataset, and
7

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Table 1: Comparison of multivariate time series forecasting results with selected deterministic baselines across various datasets. We reproduce the results for the Exchange dataset and other results of all baselines are taken from DUET and I7F
Models
TARPVAE
DUET
SOFTS
Transfoer
(3076)
75M (2025)
PuchTST
CruaSommes
DLitess (2001)
FEDiocmer (30n7yy
Maricc
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAB
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
96
0.361
0.385
0.377
1.30
0.581
0
0.386
0,415
0.401
0,412
0
0.400
0.423
0,448
0,479
0.064
0.596
0.400
0.376
0,419
Em
192
0.480
0.422
0.420
11225
0.455
0.431
0.441
0.436
0.422
0.642
0.440
0.435
0.471
0.474
0.525
0.492
0.437
0.432
0.465
336
1.455
0.645
0.471
0.680
0.452
0.487
0.858
0,892
0.005
0,691
0.462
11570
0.546
0.505
0515
0.481
0.409
1355
0.865
720
11:451
0.809
01490
11550
0.099
0.408
11503
0.491
0.500
0.000
0.487
0.411
11005
0.621
0.594
0.588
0.519
0.516
1,500
0.51
Avg
0.422
01456
0.490
165
11.233
0.329
0.297
0.347
0.207
0.549
0.310
0.361
0.286
0.340
(1.45
0.584
0.400
0.440
0.351
0.967
0.358
0.197
E1T1
192
01.359
0.382
0.364
0.389
0.573
0,394
0.380
0.400
0,40
0.410
0335
0.312
0.877
0.686
0.528
0.509
0477
0.476
0.29
0.439
376
11.291
0,419
11411
11:35
0.40
0.426
0.438
0.433
0-44
0:446
0,640
0:451
1.045
0.731
0.643
0.571
0.594
0.341
0.206
0.487
720
11.399
0.425
0.412
07236
0,433
0.427
0,645
0.441
[1450
0.436
0.453
1.108
0.763
0.574
0.679
0.831
0.657
0.403
0,474
AV6
00.355
0.372
0.29
0,573
0,400
0.383
0.407
0,402
0.477
0,385
0,410
0.942
0.694
0.611
0.550
0,559
0.515
0.437
0.449
96
0.334
0354
0325
0.361
0.314
0.365
0.523
0.365
0.329
0.365
0.404
0.345
0.372
0.379
0.419
ETTmll
193
11.661
0.37%
035%
03980
0.577
0.90
0.3m
0.99
0.890
0.394
(1:50
0.39
0.004
0.000
0.300
01426
0.461
336
0.391
0
1200
52055
(341
0.466
0.420
0.407
0.413
0.400
0.410
0,532
0.515
0.42
0:25
0413
0413
0.445
0.459
730
11446
0.435
0446
0466
03400
0.801
0.489
0.485
0:459
0:475
01455
01666
0.588
0.467
01611
0.474
0.483
0.545
0.490
Arg
113300
0
0.390
1.995
0,945
02
01407
0,410
0.35
0.007
0.396
0.400
01513
0.495
0,419
0.11
004003
01407
01.48
0.453
0.261
0180
0.204
0.182
0.306
0.203
0.287
ETTat
0.544
0.362
316
11263
0.301
13:47
0319
0,352
0.111
0.345
0.3W
0.567
0,305
0.340
01597
0,377
00437
01325
0.366
720
0.391
0.301
1:30
0.405
0.401
0.412
0.407
0.466
0.406
0.409
0.402
1.730
1.042
0.558
0,30
0.554
0.532
0.421
0.415
Avg
11.271
0,316
0.300
1.244
0.288
0.330
0.258
0.382
0.280
0.335
0.287
0.350
0.757
0.611
0.358
0.404
1 0..500
0.401
0.300
0,349
Eschinge
96
0.186
0.304
8886
02
0,90
0.211
0
0.206
0.166
0.36
0.005
0.205
0.256
0.367
0216
0098
0218
0.148
0.278
0.340
03
0.546
1.268
0,377
0.427
730
0.597
0000
10020
0,745
03447
0.599
0.685
1.195
0,645
Arg
11 11:999
0.400
0.318
0.408
0.434
0.500
0.401
0.7M
D-442
0.167
01404
(1940
0.907
0.170
0:404
00.55
01414
0.519
0.429
Bleenstt
192
0.150
11..19
0.355
0.238
0:00
0:50
0248
0255
0.233
0.248
0.14K
0.162
0,240
0.253
0.173
0.157
0.27
0.200
0.164
0.173
0.251
0.262
0.231
0.219
0.114
0.366
0217
0.39
0.30
0,197
6,996
0.265
0,282
0.195
0.201
0.315
0.30X
276
01220
0.77
0.100
0.34
0.301
0111
0.329
01202
1221
0
0.355
0.316
0.90%
0.346
0.385
0.168
0.364
2..0
0.3
0339
0.174
0.26
0.178
0.270
0.186
0.257
0.189
0.276
0.344
0.334
0.252
0.344
0.12
0.300
0.214
0.325
96
I.196
0.300
0:200
0207
0.00
0.280
0.208
0.237
0:221
0.225
0.205
0.366
0.310
0.331
0.312
0.399
0.200
0.378
0.242
0.342
Saltr
192
336
0.250
0.225
0222
0255
0228
15250
0.260
0.248
0225
0.273
0.261
0:223
0.28
0.300
0.200
0.37
0.376
0.267
0.700
01214
0.725
0.33
8-16
0353
0.200
0.415
0.398
0.292
11248
0.376
0.590
730
0.281
0.315
0.253
0.475
0.356
0,413
0:35
0.427
0.302
0.350
0.401
0.292
0.381
96
0.111
0.197
0.163
0.202
0.165
0,208
0.174
0.214
0.166
0.210
0.176
0.217
0.158
0.230
0.202
0.261
0.196
0.255
0.217
0.296
Weatha
192
112292
0.342
0.218
0217
0.283
[1211
0.544
0.215
01256
0.221
0.256
11300
0.371
0.342
0.266
0.357
01208
0.276
0.396
336
0.2622
0.289
0.274
12.5%
0.292
0.200
0.27%
0.296
0.257
11300
0.275
0.290
1272
0.335
0.257
0,335
0.283
0.335
0.339
0,390
730
0.342
0.341
0.356
0.351
0.358
0.347
0.355
0.548
0.352
0.346
0
0.351
0.
0.345
0.361
0.403
0.425
Avg
0.351
00.25
0.779
0.365
0.939
Table 2: The inference results of TARFVAE with varing sample sizes: {20, 50, 100, 2003. The CRPS is calculated using the method in Appendix A
Fachangg
Flenkiiy
Saler
Wolteer
M45
MAAD
CRFS
146F.
14AF
1056
MAA
CRPS
M4B
MEA
CRPS
3456
MAA
CRES
CRP5
345E:
MINE
CRPS
34RT
STAT
CRFE
90
40
0.300
3.15
8:314
11:.0
13.04
114
0.354
11200
0.175
0.771
0.353
0.314
1.75
1,100
1199
0.220
0.119
0.133
(3.955
200
03561
8.385
8.355
8.23
0.329
0.3%6
8331
0.303
8.349
8.399
8.338
11.997
0.369
192
0.115
8.75
3.47
8.30N
0.380
0.351
195
0361
07500
3.49
0.133
0.545
0.505
0.343
5.500
5/584
0.313
0.355
350
04410
0.42
6.343
9.505
0.345
8.300
9.341
0.39
0.229
0.391
0.112
0.294
0.335
0.59
0.366
02315
01226
8.342
6.580
6.300
01.42
0.383
336
30
3.447
3.375
0.305
0,40
0.375
0.35
1404
0.26
2335
0335
0335
0.423
0.3%
0335
0272
01204
01250
0200
0220
0.344
0.390
0.346
150
04605
8.455
0.311
8.361
0.399
0.37
8.91
6.80
0.34
8:365
0140
0.83
0.35
0353
0.300
8360
0.16
0.363
08.899
0.344
720
30
0.455
3.40
9425
0425
0.399
0481
1060
112%
2353
5339
0.5%
0354)
0334
0.56
0.367
01256
0310
0315
0344
01342
0.355
700
8.108
8.18
8.304
0.15
0.307
8.16
0.06
6.6
1001
8.40
6336
6191
0.5%
0.6
8382
0.9
0.365
01364
835
6.31
0.3
0.340
5111
0354
0.58
1.15%
1332
1/16
035
0.5%
5353
0315
0356
0353
0312
0316
(331
0331
Avg
30
3434
3.6.
9358
03505
0.355
0.35
0.94
1026
0221
2315
2311
0345
0.890
0.399
3330
1.26
0.211
01285
0349
(34)
01366
(12)
200
6447
8.41
0.55
8.355
0.367
0.381
0.391
0.30
0031
02211
8:38
8.39
0345
0.49
0.3%
8.385
01364
01219
(123)
0.44
6.36
8.35
01397
0.227
To ensure a systematic comparison of CRPS performance, we further benchmark our model against the baselines in |2 under an identical CRPS protocol. The results in Table 5 show our TARFVAE still outperforms all probabilistic and point competitors in CRPS except for ranking 2nd in one case, demonstrating the effectiveness of our generative framework. To the best of our knowledge, this work represents the first demonstration of a generative model achieving comprehensive long- term forecasting across diverse datasets (with the number of channels ranging from 7 in ETT to 321 in Flectricity) while simultaneously providing sfate-of-the-art deterministic (MSE, MAF) and probabilistic (CRPS) evaluation metrics.
8

---

Table 3: Comparison of multivariate time series forecasting results with selected generative baselines across various datasets. The results of all baselines are taken from mr- mr-Diff36].
Dutseets
ETThl
ETTml
Exchange
Eleesicity
Weather
Metric
MSE
MAE
MSE
MAB
MSE
MAE
MSE
MAE
MSB
MAE
Avg Rank
0,405
0.415
0.321
0.363
0,036
0.084
0.150
0.249 (5)
0,309
0.354
2.1
mn-Difr
B411:
0.422
0.340
0.573 (3)
0,016 (3)
0.082
0.155
0:252
0.296
0.324
2.8
DimeDief
0:402 (3)
0.430
0.336 c21
0.322
0.018 (7)
0.091
0.193
0.305 (6)
0,311
0.312 (1)
4.1
TaneKina
(1::
0.719 (16)
01874 (10)
01:05 199
0.079 (10)
(14)
0.736 (1))
0.630
(11)
(11)
14.5
CSDI
(1)
0.458 (6)
(1.)
0.442 (33)
(14)
(10)
0.356 (9
0.374 09)
11
SSSD
0.561 (14)
(14)
(90
133)
(1))
0.255 09
(8)
0.349 00
(9)
10.9
DSVAB
(3:
0.502 (11)
0.362 o9
0 19
0.200 (36)
(1))
0.286 (14)
(33)
0.375 (10)
(20)
11.3
CPP
(1:)
0.597 (16)
(19)
[14)
0.016 (1)
(3)
0.793 (09)
(44)
(1))
(17)
12.7
PSA-GIAN
ps:
0.546 (13)
0.537 (100
0.408 (13)
0.018
0.087 (7)
0.535 (14)
(14)
1.230 (10)
0.578 (10)
12.9
N-Hiss
0.4%% (3)
0.450 (2)
(7)
0.308 11
0.017 (8)
(6)
0:152 (0
(20
0.327 (5)
0.385 (M)
5.9
FiLM
0:426 (9)
0,636
0.367 69
0.376 [4)
0.016 (3)
0,079
0.210
0.300
0.336 (9)
4.8
Depts
0.579
0.691 (10)
0.380
0.412 (19
0,020
0.130
0.319 (19)
0.401 (19)
0.761 (14)
0.394
11.3
NBeats
D. p25
0.521
0.991
0:409
0.016
0.0R1
0.769
0.570
1.344
0:420
9.8
SCTNet
0:465
0:463
0:389
0.389
0:036
0.137
0.171
0.250
0.329
0.344
8
NLinear
0,410
0.418
0.349
0.375
0:019
0.091
0.147
0.239
0.313
0.328
4.2
DLinnar
0:415 m
0.442
0.345 cB
0.578
0,022
0.102
0.215
0.336 (8)
0.485 (12)
0.444
8.6
LSTMa
1,149 (22)
0,782 (37)
1.030
0.689 (02)
0:403 (35)
0.534 (17)
0.414 (13)
0:444
0.652 (10)
0.501
15.6
Table 4: The inference time (in ms) of various time series generative models with different prediction lengths on the univariate ETTh1 dataset. The results of all baselines are taken from [if-iff3)))
inference (126)
TAREVAE sumples
2.9
3.01
2,8
3.0
TARFVAR: (2 samples -00
3.2
3.1
3.1
3.2
TARPVAE (#f samples 200)
3.2
3.2
3.1
3.2
S-2
9.8
11.9
21.6
TimeDiff
17.6
26.5
34.6
TimeGrad
870.2
1854.5
3119,7
6724.1
CSDI
90.4
142,8
398.9
$13.1
SSSD
418.6
645.3
1054,2
2516.9
5.3
Ablation study
In this part, we conduct experiments using the exact same configuration as the main experiments, modifying only the targeted settings for analysis to ensure the consistency and reliability of the conclusions.
Influence of lookback windows. Figure 3 the performance of TARFVAE with varying lookback window lengths. Overall, TARFVAE consistently achieves superior performance across all evaluated lookback windows, with its accuracy improving as the length gets longer. Notably, on the
Table 5: CRPS comparison following ProbTS 27 protocol: TARFVAE vs. best baselines. The results of all baselines taken from [2]
Dotaset
Pred
CRPS
TARFVAE
Other Top Performunce
96
0.233
0.236 (CSDD)
ETTml
336
192
0.261
0.264
(1332 (CSDS)
1.291 (CSDS)
730
0.291
0L353 (PishTST)
96
0.110
0. (CSDI)
ETTm2
192
0.150
0.131
176 (PacchTSTT)
147 (CSDI)
730
0.171
01205 (PaicTTTT)
0.254
0.359 (Thonsfommr)
193
0.27%
PeechTSTT)
356
0.301
730
0.318
0.397 (PachTST))
96
0.150
0.164 (CSDI)
ETT22
336
192
EL185
(1173
(.201 (Pacch (ST))
(1240 (Path
730
0.190
0,252 (Pu)hTSTT)
96
EL068
0.886 (Paxch TST)
Flectricity
316
192
[U181
IU177
0.999 (GRU NVP)
0.992 (Parhh ISTT)
730
0U187
0.10 (TimeTlna))
96
BJ665
0.068 (CSDS)
Weather
192
316
0.070
0.174
0.868 (CSD))
0.81 (CSD3)
730
(L080
0.087 (CSD))
0.119
0U023 (PuxhTST)
Eschange
0
0,011
0,048 ('Trandormer
0.034 (PuchTST)
DLiinar)
E.072 (PTI

---

ETTm2 dataset, TARFVAE exhibits sustained performance enhancement with increasing window lengths, while competing methods show clear saturation effects.
KTTml
ETTm2
Weather
0.55
PachEST
Tree besne SUITS
Times for
0.50
SuFTs
Barthak
la fuu
0.28
0.40
0.26
0.35
96
192
356
%6
192
356
192
336
Lookhock Windew Leugth
Lookback Window Length
Lookback Window Length
Figure 3: Influence of lookback window length L.
Table 6: Ablation study on various datasets. The results are averaged from forecast horizons
H {96, 192, 336, 720) for all datasets with a fixed lookback window length L 96.
P7TB1
Befhenge
Blenkkyy
Weathr
Mark
MS0:
MAR
MS2
MAR
MSE
MAII
MMI
MAR
MSD
MAG:
MSS
MAR
MSSE
MAR
MAR
MSB
MAT:
VARPNAE
6432
0.354
0.39
0,855
0.564
0.3M
0.275
0.306
8,547
0.307
0.30
0.206
14235
11297
IL243
0.200
0.301
0,503
wit TARFLIR LWW
0:411
0.411
0.37
6.031
0.996
0.00
0.279
9.50u
9:420
0.33
0.100
0.78
0.16
0.300
0:333
0.330
0.332
0.231
We MABETARFLOW
8468
8439
0.365
6440
0.944
0/417
0.99
0.542
3.40
0.32
0.136
0.33
0238
I1340
0.276
0.334-18-39
0.340
Architecture ablations. As evidenced in T removing the TARFLOW component and further eliminating VAE lead sustained deterioration. These findings collectively demonstrate that the synergistic integration of TARFLOW with VAE critically enables TARFVAE's superior modeling capacity.
Influence of inference sample size. Upon completing model training, we evaluate TARFVAE's
inference performance under varying sample sizes, shown in Table As the sample size increases from 20 to 200, the reduced sampling bias consistently improves the MSE, MAE and CRPS. The absence of significant metric fluctuations across different sample sizes confirms the stability of TARFVAE's performance. These collective findings substantiate that TARFVAE achieves both reliable uncertainty quantification and deterministic modeling with strong operational stability.
6 Conclusion
In this work we present TARFVAE, an efficient one-step generative framework for time series forecasting. It integrates TARFLOW with VAE architecture to enhance posterior estimation, enabling the learning of a more expressive latent space which can lead to efficient modeling of the targeted time series distribution. Implemented on an simple MLP foundation in our extensive experiments, TARFVAE achieves superior or comparable performance to recent state-of of tftte-of-thearrr deterministic and generative models across widely-used real-world benchmarks. To our knowledge, this the first time a generative time series forecasting model delivers comprehensive long-term predictions consistent with deterministic methods on rich datasets, encompassing both deterministic (MSE, MAE) and probabilistic (CRPS) forecasting metries. Mcanwhile, TARFVAE's one-step generation reduces inference time by over 85% compared to other state-of-the-art generative models in long-term forecasting, Other implementations could be tried to achieve better performance in the future.
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[42] Syama Sundar Rangapuram, Shubham Kapoor, Rajbir Singh Nirwan, Pedro Mercado, Tim Januschowski, Yuyang Wang, and Michael Johlke-Schneider Coherent probabilistic forecasting of temporal hicrarchies. In International Conference on Artificial Intelligence and Statisties, pages 9362-933 9376. PMLR, 2023.
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A Calculation of CRPS
After the inference of sufficient samples, we employ an efficient quantile-based approach to caleu- late CRPS. This aims to mitigate computation costs in estimating CRPS with all samples. Given certain quantiles (9). Q2, .... Jn]. we first sort these samples and extract corresponding quantile values [Q()), Q(12)..... (g.)), then compute CRPS using the following formulation:
q2,...
CRPS = f 2. (Q()) y) -T(( S Q(())) g)dqq
(29)
We adopt constant extrapolation, that is Q(1) Q(qi), V4 qı and Q(4) Q((nn, Vy qn Thus, (29) can be further formulated as
4 = 2 (Q(() - 5) (T(y s Q(ai)) - -1d4
CRPS
(30)
0
4n
2. (Q(4)) 9) (T Q(a)) pddq
(31)
2. (Q(ga) v) -T(y Q(a,)) - g)dg.
(32)
As for 30 it equals to
(Q())) 9) (91 0.5g
y ك Q(q));
(33)
2. (Q(a)) - y) (-0.5gf),
y > (()).
As for 32
it equals to
2 1. (Q(nn) - v) (0.5(1 - )2)
y S Q(m)):
(34)
2 (Q(m)) y) (-0.5(1 ))
y > Q(4)).
As for 31 b1, it is discretized and approximated as
2. Σ (Q(a)) - y) (I(v S Q(4:)) q:) Ag.
(35)
The inplementation of this calculation process can be found in our code.
B Limitations and Future Works
We analyze the limitations of our work and briefly discuss several directions for future research. In our work, we employ identical MLP blocks for the encoder, decoder, and prior modules. This configu- ration might limit the forecasting performance of the proposed TARFVAE model. For instance, since the encoder, decoder, and prior typically perform different functions, we may flexibly design distinct architectures for these three components. Moreover, MLP blocks may not be sufficiently powerful to effectively extract time series patterns from the input data, potentially hindering TARFVAE's 's ability learn complex time series patterns. In the future, exploring advanced temporal processing modules or deep learning models within the TARFVAE framework could be beneficial.
C Societal Impacts
Extensive experiments on real-world datasets demonstrate the TARFVAE's potential capability to significantly benefit various application fields, spanning from finance to energy, by providing accurate and reliable forecasts. However, there are potential negative societal impacts to consider. As model that often interacts with sensitive and proprietary data, particularly in sectors like healthcare and finance, TARFVAE could inadvertently contribute to privacy risks if the data it processes is not adequately protected. Moreover, Organizations might also become overly reliant on automated forecasts, neglecting valuable insights from human experts, which can affect decision quality. To prevent the aforementioned negative societal impacts, data integrity and security strategies should be well-designed to ensure the deployment of TARFVAE enhances beneficial societal effects while reducing possible adverse impacts.
21


Reviews:
[{"review_id": "4YogJAD5at", "reviewer": "Reviewer_QEJx", "summary": "This paper introduces a new generative model for time-series forecasting, where the key idea is to combine autoregressive flow with autoencoder to achieve efficient one-step generation.", "questions": "- Please explain why you only compare with point forecasting models and mainly employ the point estimation metrics.\n- Please add necessary related studies in studying generative time-series forecasting models and comparing point and probabilistic forecasting paradigms.\n- Please add necessary experimental results to support your core claims.", "limitations": "See the weakness part.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n- Overall, I think this is a good paper, introducing an **efficient** generative model for time-series forecasting.\n- Specifically, I like Section 4.2 MLP Foundation, which attempts to seperate the confounding effects of different network architectures as this paper mainly focuses on the generative forecasting framework. \n\nWeaknesses\n\n- My major concerns stem from the facts that although this paper proposes a generative forecasting framework, it **merely compares with recent point forecasting models** and **mainly consider point forecasting metrics**.\n  - Typically, point and probabilistic forecasting studies evolve in their respective research threads and rarely mix with each other's branch. Recently, https://arxiv.org/abs/2310.07446 provided a systematic study comparing these two research branches, and according to their analyses, one major disadvantage of existing probabilistic forecasting methods lies in their inefficiency because many of them mainly considered short-term forecasting.\n  - From the efficiency perspective, I think this paper has addressed a pain point of existing probabilistic models, but the experimental parts do not involve comparisons with previous probabilistic forecasting models.\n  - If this paper focuses on generative models, delivering probabilistic forecasts rather than point forecasts, why the main experimental comparisons (Table 1) are presented using point metrics, such as MSE and MAE? Only in Table 2, I have found the results using the CRPS metrics, while only the results of TARFVAE have been provided. There is no performance comparisons with other models. Intuitively, the experimental comparisons in CRPS should be the core experiments to demonstrate the effectiveness of your proposed generative model.", "was_revised": true, "final_justification": "Author's rebuttal looks good to me. Developing an efficient yet effective probabilistic forecasting method has always been a grand challenge in the time-series field, especially when forecasting horizons or variables are large. This work has made some progresses on this way.", "rebuttal": "Thank you for your thoughtful feedback and recognition of our work. We address your concerns below:\n\n**1. Comparison scope and metrics:**\n\nWe intentionally compared our generative framework with **both state-of-the-art point forecasting models (Table 1) and generative/probabilistic models (Table 3)**. We used MAE/MSE as unified metrics because:\n\n- they are widely reported across both forecasting paradigms, enabling fair cross-paradigm accuracy comparison;\n\n- they mitigate reproducibility discrepancies (e.g., mr-Diff, one of our generative baselines, only reports MAE/MSE, and lacks public code);\n\n- as noted in the paper[1] you mentioned, MAE is also adopted as a standard benchmark for probabilistic methods.\n\nSome probabilistic baselines (e.g., mr-Diff, TimeDiff) either omit CRPS for long-horizon tasks (could face extreme computational constraints) or lack public code, which makes comprehensive CRPS evaluation difficult. Nevertheless, to the best of our knowledge, ours is one of the first—and possibly the only—generative time-series forecasting works to **report MAE/MSE/CRPS at long horizons across such diverse datasets (Table 2), with full code released to facilitate any further research**. Moreover, in response to your feedback, **we add CRPS comparison following ProbTS[1] below** as it extended the evaluation of some current probabilistic methods to the long-term.\n\n**2. Related work:**\n\nWe adopted state-of-the-art generative models (e.g. mrDiff, TimeDiff, TimeGrad, CSDI...) as baselines and have reviewed them in **Related Work**. We also explicitly contrasted probabilistic vs. point forecasting paradigms in **Introduction**, noting probabilistic methods further quantify uncertainty through distributional estimation. Current studies within these two paradigms, as Zhang et al.[1] indicated, differ in standardization, generation methods, and forecasting lengths. Zhang's work extended the evaluation of some probabilistic methods to the long-term and conducted a comprehensive comparison between the two paradigms. We will include the suggested paper[1] to enrich this discussion in later version. We've also compared our results with Zhang's, as shown in the next response.\n\n**3. CRPS results:**\n\nFollowing your suggestion, we benchmark our model against baselines in ProbTS[1] (including both point and generative/probabilistic models) using the identical CRPS protocol. We produce this new CRPS without retraining, and the baseline results are taken from Table 10 in [1]. **Results below show our TARFVAE still outperforms all probabilistic and point competitors in CRPS except for ranking 2nd in one case, demonstrating the effectiveness of our generative framework.**\n\n**Table: CRPS results following identical protocol of ProbTS. Baseline results are taken from ProbTS. Bold numbers indicate the best performance.**\n| Dataset | Horizon | TARFVAE (ours)| Other Top Performance |\n|:---|:---|:---|:---|\n| ETTm1 | 96 | **0.222** | 0.236(CSDI) |\n|  | 192 | **0.244** | 0.291(CSDI) |\n|  | 336 | **0.261** | 0.322(CSDI) |\n|  | 720 | **0.291** | 0.353(PatchTST) |\n| ETTm2 | 96 | **0.110** | 0.115(CSDI) |\n|  | 192 | **0.131** | 0.147(CSDI) |\n|  | 336 | **0.150** | 0.176(PatchTST) |\n|  | 720 | **0.171** | 0.205(PatchTST) |\n| ETTh1 | 96 | **0.254** | 0.321(iTransformer) |\n|  | 192 | **0.278** | 0.359(iTransformer & PatchTST) |\n|  | 336 | **0.301** | 0.384(PatchTST) |\n|  | 720 | **0.318** | 0.397(PatchTST) |\n| ETTh2 | 96 | **0.150** | 0.164(CSDI) |\n|  | 192 | **0.173** | 0.201(PatchTST) |\n|  | 336 | **0.185** | 0.240(PatchTST) |\n|  | 720 | **0.190** | 0.252(PatchTST) |\n| Electricity | 96 | **0.068** | 0.086(PatchTST) |\n|  | 192 | **0.077** | 0.092(PatchTST) |\n|  | 336 | **0.081** | 0.099(GRU NVP) |\n|  | 720 | **0.087** | 0.108(TimeGrad) |\n| Weather | 96 | **0.065** | 0.068(CSDI) |\n|  | 192 | 0.070 | **0.068(CSDI)** |\n|  | 336 | **0.074** | 0.083(CSDI) |\n|  | 720 | **0.080** | 0.087(CSDI) |\n| Exchange | 96 | **0.019** | 0.023(PatchTST) |\n|  | 192 | **0.028** | 0.034(PatchTST) |\n|  | 336 | **0.041** | 0.048(iTransformer & PatchTST & DLinear) |\n|  | 720 | **0.068** | 0.072(PatchTST) |\n\nReferences:\n\n[1] Zhang et al. \"ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizons\". NIPS 2024."}, {"review_id": "5jLpsjbfsR", "reviewer": "Reviewer_zanJ", "summary": "The work proposes TARFVAE, an approach that integrates transformer-based auto-regressive flows (TARF) with VAE, for time series forecasting task. It uses TARFs to model variational posterior latent distributions which are more expressive than parameterized Gaussian distributions, which is typically used in VAE. The approach also permits one-step generation for future forecasting, achieving great computational efficiency. As a generative model, the proposed approach shows performance and efficiency superior to both deterministic and generative models on various time series datasets, particularly in long-term forecasting.", "questions": "Please see the weakness section.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths:\n1. Experiment results on standard benchmark datasets outperformed the SOTA models while preserving generation capability and great computational efficiency due to one-step generation. The experiment results provides solid support to the claimed contributions of the work.\n2. The work provides rich technical details when describing the TARFVAE method. The presentation is easy to follow and read.\n\n## Weakness:\n1. My biggest concern of the work is the limited novelty despite its superior performance and computational efficiency. The approach of using normalizing flows to model the variational posterior distribution in VAE has been explored in previous works [1]. The work can be positioned as an work that extend this approach to the time-series domain.\n2. The major experiment results are based on an MLP architecture proposed in the work. Exploring other model architectures like transformers could both highlight the generalizability and flexibility of the work and makes the experiment results more solid.\n\nReferences:\n\n[1] Rezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" ICML 2015", "was_revised": true, "final_justification": "I'm still not completely satisfied with the limited novelty and plain contributions of the work. Overall speaking, the work is much more solid after my concerns were addressed by the author.", "rebuttal": "Thank you for the detailed comments. We appreciate your concerns and address them as follows:\n\n**1.Novelty through Cross-Domain Innovation & Advancement:**\n\nWhile [1] pioneered flows in VAEs, our work **introduces key innovations**:\n\n- further employing Transformer-based autoregressive flows (TarFlow) to strenthen VAE posterior approximation;\n\n- strategic use of TarFlow's unidirectional flow enabling efficient one-step generation without compromising expressiveness. This avoids the costly bijective inversion at inference, yielding a significant efficiency gain over standard flow-VAEs.\n\n- first application of flow-VAE integration to generative time-series forecasting.\n\nCross-domain adaptation is fundamental to research progress. As Transformers migrated from NLP to CV, AI and beyond, enabling new capabilities and deeper understanding, our work **demonstrates how advancing flow-VAEs in time-series**:\n\n- solves unique challenges (long-horizon forecasting);\n\n- reveals new efficiency-performance tradeoffs (one-step generation with high quality); \n\n- establishes competitive alternatives to domain-specific architectures (SOTA performance).\n\nOur work **aligns with recent related efforts to re-explore underutilized previous ideas**:\n\n- A decade after [1], [2] revisited flows and pretrained VAEs for efficient one-step image generation.\n\n- Despite diffusion models' dominance, TarFlow[3] revived interest in flows by demonstrating state-of-the-art image generation (though building on IAF[4]).\n\n- While diffusion models and recurrent VAEs dominate generative time-series forecasting via computationally intensive multi-step generation, our TARFVAE framework achieves superior efficiency and performance through one-step generation.\n\n**2.MLP Architecture Choice:**\n\nAs noted by Reviewer QEJx, we intentionally used a simple MLP backbone to isolate the contribution of our generative framework and avoid confounding effects from other complex modules. This design clearly demonstrates the efficacy of our core method.\n\nFollowing your suggestion, **we replace the MLP backbone used in our original experiments with iTransformer** and conduct a quick evaluation on the ETTm and Exchange datasets; the outcomes are shown below. The new configuration matches the original in overall quality, continuing to surpass other competitors in most settings. Specifically, it enjoys an edge over the original model when the horizon is short (e.g. on ETTm1 and Exchange at horizons of 96 and 192), whereas it falls slightly behind when the horizon is long. This nuanced difference is difficult to interpret conclusively; one plausible explanation is that iTransformer, being more complex than the MLP, induces slight overfitting on longer horizons. Taken together, these findings further **underscore the generalizability and flexibility of our approach and suggest that the proposed generative framework empowered by TarFlow’s potent distribution transformations already suffices to achieve state-of-the-art performance**.\n\n**Table: Results of original TARFVAE and iTransformer alternative. In comparisons between each TARFVAE and the other models, the best result is indicated in bold.**\n\n| Model |  | TARFVAE |  | TARFVAE-iTransformer|  | Other Top Performance |  |\n|:---|:---|:---|:---|:---|:---|:---|:---|\n| Metric |  | MSE | MAE | MSE | MAE | MSE | MAE |\n| ETTm1 | 96 | **0.311** | **0.351** | **0.306** | **0.350** | 0.323(TSMixer) | 0.354(DUET) |\n|  | 192 | **0.361** | **0.378** | **0.356** |**0.378** | 0.369(DUET) | 0.379(DUET) |\n|  | 336 | **0.391** | **0.401** | **0.391** | 0.404 | 0.400(PatchTST) | **0.402(DUET)** |\n|  | 720 | **0.456** | **0.435** | **0.458** | 0.441 | 0.463(DUET) | **0.437(DUET)** |\n|  | Avg | **0.380** | **0.391** | **0.378** | **0.393** | 0.390(DUET) | 0.393(DUET) |\n| ETTm2 | 96 | **0.171** | **0.249** | **0.171** | **0.252** | 0.174(DUET) | 0.255(DUET) |\n|  | 192 | **0.229** | **0.291** | **0.237** | **0.296** | 0.243(DUET) | 0.302(DUET) |\n|  | 336 | **0.293** | **0.334** | **0.301** | **0.341** | 0.304(DUET) | 0.341(DUET) |\n|  | 720 | **0.391** | **0.391** | **0.399** | **0.396** | 0.399(DUET) | 0.397(DUET) |\n|  | Avg | **0.271** | **0.316** | **0.277** | **0.321** | 0.280(DUET) | 0.324(DUET) |\n| Exchange | 96 | **0.086** | **0.204** | **0.083** | **0.202** | 0.086(DUET & iTransformer) | 0.205(DUET & PatchTST) |\n|  | 192 | **0.172** | **0.294** | **0.170** | **0.294** | 0.176(PatchTST & DLinear) | 0.299(iTransformer & PatchTST) |\n|  | 336 | 0.340 | 0.423 | 0.320 | 0.410 | **0.301(PatchTST)** | **0.397(PatchTST)** |\n|  | 720 | 0.797 | 0.678 | 0.855 | 0.691 | **0.654(TSMixer)** | **0.624(DUET)** |\n|  | Avg | 0.349 | 0.400 | 0.357 | 0.399 | **0.318(DUET)** | **0.384(DUET)** |\n\n\nReference:\n\n[1] Rezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" ICML 2015.\n\n[2] Zhengyang Geng et al. \"Mean Flows for One-step Generative Modeling\". 2025.\n\n[3] Zhai et al. \"Normalizing Flows are Capable Generative Models\". ICML 2025.\n\n[4] Kingma et al. \"Improving Variational Inference with Inverse Autoregressive Flow\". NIPS 2016."}, {"review_id": "T652QVoXXY", "reviewer": "Reviewer_3TPd", "summary": "The paper proposes to treat time series prediction as conditional generation: given a lookback history, e.g. 96 consecutive observations, one may predict the next observations up to a prespecified horizon e.g. 192 observations. In such a setting, one may use the conditional VAE architecture where the historical observations are given as conditioning input, this defines a distribution in latent space from which we sample and decode to produce the full matrix of horizon predictions in one neural network pass. Sampling multiple latents and decoding yields multiple output predictions.\n\nThis is contrast to autoregressive methods that must compute predictions up to a horizon time step by time step each requiring a network pass, or diffusion that requires iterative denoising where each denoising step is a single network pass.\n\nAt a high level the method uses the standard C-VAE components, similar to a standard VAE however a conditioning  variable informs the prior over latent variable and the likelihood (decoder) and also the approximate posterior over the latent variable (encoder). Typically the approximate posterior is takes observed data as input and returns an isotrpoic Gaussian distribution, this work uses a Normalizing Flow model that incorporates a transformer, TARFLOW. During training, the past data and future data is passed to the encoder, the TARFLOW approximate posterior, the ELBO is used to inform the approximate posterior to align with the Gaussian prior (determined lookback data) and the likelihood of the output data (decoder reconstruction).\n\nAt inference time, the lookback data is used to inform the Gaussian prior over latent variables, a latent vector is sampled, and the lookback data as well as the sampled latent value are decoded to yield a matrix of predictions for the time series up to the horizon. The TARFLOW model is not required.\n\nExperiments are performed on a range of datasets from the literature and show favorable performance against a range of recent methods from the literature.", "questions": "- how to handle test time sequences shorter than the lookback duration?\n- can the authors report mean MSE and MAE in line with the results copied from SOFTS and DUET?\n- can the authors elaborate on why a Conditional-VAE outperforms diffusion somewhat opposing the community consensus that diffusion", "limitations": "- input and outpout shapes are fixed during training (which is true for some diffusion methods too)", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "# Strengths\n- the approach seems simple, elegant, a Conditoinal VAE that uses modern architectures.\n\n# Weaknesses\n- fixed time length, auto regressive for longer time series than the model was trained for still requires multiple forward passes, can the model be used for settings where the lookback is shorter than whaat was trained? (Presumably the same limitation applies to diffusion based methods)\n- where is the baseline mrDIFF?\n- it seems the SOFTS and DUET authors report the mean of MSE and MAE of predictions, whereas this work shows the median. This makes the results not comparable (arguably median may be lower as it negates large MSE outliers and MSE>0 bounds low MSE outliers). If the mean MSE, MAE are still outperforming baselines, then I will happily raise my score.\n\n## Minor Comment\n- is it possible to see the MSE per time step? Does the MSE grow with time?\n- the hypothesis of the paper seems strange. In generative modeling, in the last few years, iterative refinement methods, using autoregression or diffusion, have been outperforming one-shot methods like VAEs and GANs. This paper argues that the Gaussian approximate posterior is to blame and simply making the approximate posterior more flexible during training gives it the advantage. I realise this is high level and speculative and the ablation study removing TARFLOW shows a decrement, but it may be worth acknowledging or discussing and make the paper more convincing: a more flexible approximate posterior can make VAEs outperform diffusion apparently.\n- the notation switch of learning $(x,y)$ in Sectoin 3 to $(x, y)$ in section 4 was rather confusing at first", "was_revised": true, "final_justification": "All of my issues have been resolved. My main concern was the reported metric for which I had partly misunderstood and has been satisfactoraly cleared up.", "rebuttal": "Thank you for the helpful comments. Below we address each concern:\n\n**1. Variable-length lookback / horizon:**\n\nLike most LTSF models, ours is trained with fixed lengths. For test sequences shorter than the trained lookback window, common solutions include:\n\n- retraining on the desired window;\n\n- padding (e.g., padding at the beginning, as in Crossformer[1]);\n\n- adopting placeholder tokens and masking mechanisms for variable-length inputs (e.g., MOIRAI [2], ElasTST [3]).\n\nOur framework can readily incorporate similar mechanisms for flexible forecasting.\n\n**2. mr-DIFF baseline:**\n\nResults for mr-DIFF are included in Table 3 (accuracy) and Table 4 (inference speed). We confirm no baseline was omitted.\n\n**3. Metric reporting (Mean vs. Median):**\n\nWe clarify that our reported MAE/MSE values are averages over the entire forecast horizon, identical to SOFTS and DUET. The term **'median' refers only to the median over multiple stochastically generated samples** of the same model (i.e., we report the performance of median across generated samples). Table 2 demonstrates the robustness of this sample median. For direct comparison, we are willing to **report the corresponding mean-over-samples scores below**. The results demonstrate that while the mean performance is marginally weaker than the median (sometimes also better, e.g. Exchange 192), they remain closely aligned. Nevertheless, **both significantly outperform other baseline models**.\n\n**Table A: TARFVAE's results of median (the original) and mean over the same generated samples. In comparisons between each TARFVAE and the other models, the best result is indicated in bold.**\n| Model |  | TARFVAE |  | TARFVAE-mean |  | Other Top Performance |  |\n|:---|:---|:---|:---|:---|:---|:---|:---|\n| Metric |  | MSE | MAE | MSE | MAE | MSE | MAE |\n| ETTh1 | 96 | **0.360** | **0.388** | **0.360** | **0.388** | 0.376(FEDformer) | 0.393(DUET) |\n|  | 192 | **0.410** | **0.422** | **0.410** | **0.423** | 0.420(FEDformer) | 0.425(DUET) |\n|  | 336 | **0.455** | **0.445** | **0.455** | **0.446** | 0.459(FEDformer) | 0.446(DUET) |\n|  | 720 | **0.481** | **0.469** | **0.484** | **0.470** | 0.487(PatchTST) | 0.479(PatchTST) |\n|  | Avg | **0.427** | **0.431** | **0.427** | **0.432** | 0.440(FEDformer) | 0.436(DUET) |\n| ETTh2 | 96 | **0.273** | **0.329** | **0.273** | **0.329** | 0.288(PatchTST) | 0.340(PatchTST) |\n|  | 192 | **0.359** | **0.383** | **0.359** | **0.382** | 0.368(DUET) | 0.389(DUET) |\n|  | 336 | **0.391** | **0.409** | **0.392** | **0.410** | 0.410(SOFTS) | 0.422(DUET) |\n|  | 720 | **0.399** | **0.428** | **0.399** | **0.428** | 0.411(SOFTS) | 0.433(SOFTS) |\n|  | Avg | **0.356** | **0.387** | **0.356** | **0.387** | 0.372(DUET) | 0.398(DUET) |\n| ETTm1 | 96 | **0.311** | **0.351** | **0.312** | **0.352** | 0.323(TSMixer) | 0.354(DUET) |\n|  | 192 | **0.361** | **0.378** | **0.362** | **0.378** | 0.369(DUET) | 0.379(DUET) |\n|  | 336 | **0.391** | **0.401** | **0.391** | **0.401** | 0.400(PatchTST) | 0.402(DUET) |\n|  | 720 | **0.456** | **0.435** | **0.457** | **0.436** | 0.463(DUET) | 0.437(DUET) |\n|  | Avg | **0.380** | **0.391** | **0.380** | **0.392** | 0.390(DUET) | 0.393(DUET) |\n| ETTm2 | 96 | **0.171** | **0.249** | **0.171** | **0.250** | 0.174(DUET) | 0.255(DUET) |\n|  | 192 | **0.229** | **0.291** | **0.230** | **0.293** | 0.243(DUET) | 0.302(DUET) |\n|  | 336 | **0.293** | **0.334** | **0.296** | **0.336** | 0.304(DUET) | 0.341(DUET) |\n|  | 720 | **0.391** | **0.391** | **0.397** | **0.394** | 0.399(DUET) | 0.397(DUET) |\n|  | Avg | **0.271** | **0.316** | **0.273** | **0.318** | 0.280(DUET) | 0.324(DUET) |\n| Exchange | 96 | **0.086** | **0.204** | **0.086** | **0.204** | **0.086(DUET & iTransformer)** | 0.205(DUET & PatchTST) |\n|  | 192 | **0.172** | **0.294** | **0.170** | **0.293** | 0.176(PatchTST & DLinear) | 0.299(iTransformer & PatchTST) |\n|  | 336 | 0.340 | 0.423 | 0.327 | 0.416 | **0.301(PatchTST)** | **0.397(PatchTST)** |\n|  | 720 | 0.797 | 0.678 | 0.822 | 0.689 | **0.654(TSMixer)** | **0.624(DUET)** |\n|  | Avg | 0.349 | 0.400 | 0.351 | 0.400 | **0.318(DUET)** | **0.384(DUET)** |\n| Electricity | 96 | **0.139** | 0.238 | **0.140** | 0.239 | 0.143(SOFTS) | **0.233(DUET & SOFTS)** |\n|  | 192 | 0.159 | 0.255 | 0.161 | 0.257 | **0.158(SOFTS)** | **0.248(DUET & SOFTS)** |\n|  | 336 | **0.173** | 0.270 | 0.176 | 0.271 | 0.175(DUET) | **0.262(DUET)** |\n|  | 720 | **0.202** | 0.294 | 0.206 | 0.295 | 0.204(DUET) | **0.291(DUET)** |\n|  | Avg | **0.168** | 0.264 | **0.171** | 0.265 | 0.172(DUET) | **0.259(DUET)** |\n| Solar | 96 | **0.195** | 0.220 | **0.195** | 0.224 | 0.200(DUET & SOFTS) | **0.207(DUET)** |\n|  | 192 | **0.225** | 0.242 | **0.227** | 0.245 | 0.228(DUET) | **0.233(DUET)** |\n|  | 336 | 0.250 | 0.262 | 0.254 | 0.264 | **0.243(SOFTS)** | **0.244(DUET)** |\n|  | 720 | 0.254 | 0.269 | 0.257 | 0.270 | **0.245(SOFTS)** | **0.249(DUET)** |\n|  | Avg | 0.231 | 0.248 | 0.233 | 0.251 | **0.229(SOFTS)** | **0.233(DUET)** |\n| Weather | 96 | **0.151** | **0.197** | **0.155** | **0.201** | 0.158(Crossformer) | 0.202(DUET) |\n|  | 192 | **0.202** | **0.242** | 0.209 | **0.247** | 0.206(Crossformer) | 0.252(DUET) |\n|  | 336 | **0.262** | **0.289** | **0.270** | **0.294** | 0.272(Crossformer) | 0.294(DUET) |\n|  | 720 | **0.342** | **0.341** | **0.347** | **0.343** | 0.349(DUET) | 0.343(DUET) |\n|  | Avg | **0.239** | **0.267** | **0.245** | **0.271** | 0.251(DUET) | 0.273(DUET) |\n| Count 1st |  | 33 | 27 | 30 | 27 |  |  |\n\n**4. Per-timestep MSE:**\n\nAs requested, we **provide some detailed per-timestep MSE (see below)**. As expected, MSE generally increases with prediction horizon (periodic fluctuations may occur in datasets with inherent seasonality, such as ETTm1, which can be easily discerned from the plot), aligning with the intuition that distant forecasts are more challenging.\n\n**Table B: Detailed per-timestep MSE. We take Electricity, Exchange and ETTm1 with horizon=720 for example, and report results every 50 steps to shorten the table.**\n| Step (of horizon=720) | Electricity | Exchange | ETTm1 |\n|:---|:---|:---|:---|\n| 1 | 0.088 | 0.023 | 0.075 |\n| 51 | 0.145 | 0.114 | 0.35 |\n| 101 | 0.157 | 0.223 | 0.338 |\n| 151 | 0.171 | 0.355 | 0.404 |\n| 201 | 0.19 | 0.481 | 0.399 |\n| 251 | 0.189 | 0.587 | 0.442 |\n| 301 | 0.196 | 0.705 | 0.47 |\n| 351 | 0.214 | 0.83 | 0.502 |\n| 401 | 0.22 | 0.938 | 0.492 |\n| 451 | 0.217 | 1.041 | 0.503 |\n| 501 | 0.219 | 1.083 | 0.523 |\n| 551 | 0.232 | 1.133 | 0.541 |\n| 601 | 0.242 | 1.22 | 0.543 |\n| 651 | 0.251 | 1.387 | 0.54 |\n| 701 | 0.266 | 1.489 | 0.568 |\n\n**5. Why C-VAE:**\n\nWhile iterative refinement methods like diffusion gained popularity for high-fidelity generation, their inherently iterative nature incurs **substantial computational costs**. This has **spurred renewed interest in one-step generation** paradigms. Recent studies (e.g., Mean Flows[4], OSV[5]) ultilize pretrained VAEs/GANs and achieve high-quality image/video generation through efficient latent-space discrimination in a single step. Their success suggests that **well-structured latent spaces may inherently contain sufficient information for high-quality generation**. When unlocked through task-specific constraints (e.g., flow matching identities, adversarial discriminators), the information enables high-fidelity one-step mapping.\n\nSimilarly, for our proposed TARFVAE, we posit that **Transformer-based autoregressive flows (TarFlow) enhances the VAE encoder by enriching the latent space's informational capacity**, forming the foundation for improved quality. This also **boosts the decoder to specialize in latent-variable discrimination and master one-step mapping** (since VAE encoder and decoder implicitly learn in an inherent adversarial way). Compared to diffusion models where each step approximates a local Gaussian assumption, we posit that an one-step model can match or surpass diffusion performance — **provided the sufficient expressiveness of latent space (always non-Gaussian) and potent latent-variable discrimination, the information flux of a single step can compete that accumulated over multiple steps**.\n\nReference:\n\n[1] Yunhao Zhang, Junchi Yan. \"Crossformer: Transformer Utilizing Cross-Dimension Dependency for Multivariate Time Series Forecasting\". ICLR 2023.\n\n[2] Woo et al. \"Unified Training of Universal Time Series Forecasting Transformers\". PMLR 2024.\n\n[3] Jiawen Zhang. \"ElasTST: Towards Robust Varied-Horizon Forecasting with Elastic Time-Series Transformer\". NeurIPS 2024.\n\n[4] Zhengyang Geng et al. \"Mean Flows for One-step Generative Modeling\". 2025.\n\n[5] Mao et al. \"OSV: One Step is Enough for High-Quality Image to Video Generation\". CVPR 2025."}, {"review_id": "cqO6OqmX2G", "reviewer": "Reviewer_EWqS", "summary": "This paper proposes TARFVAE, a novel generative framework for time series forecasting that combines Transformer-based autoregressive flow (TARFLOW) with variational autoencoders (VAE). The key innovation is enabling efficient one-step generation for long-term forecasting by using only the forward process of TARFLOW to enhance VAE's posterior estimation, avoiding computationally expensive autoregressive inverse operations while breaking the Gaussian assumption for more informative latent representations.", "questions": "1. Why choose MLP decoders over more expressive architectures for complex temporal patterns?\n2. How does the method scale with very long input sequences or forecast horizons?\n3. The claim that complex architectures aren't necessary needs stronger justification. Have you tested more complex alternatives?", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1.  The paper addresses a genuine limitation in current generative time series forecasting - the computational inefficiency of recurrent operations and repeated denoising steps.\n2. The combination of normalizing flows with VAE for time series forecasting is creative. The specific innovation of using only the forward process of TARFLOW to enhance posterior estimation while avoiding inverse operations is technically sound and addresses the efficiency concerns. \n3. The one-step generation capability could be particularly valuable for real-world applications where prediction speed matters.\n4. The proposed method outperforms both deterministic and generative SOTA across multiple benchmarks.\n\nWeaknesses:\n\n1. The decision to integrate Transformer architecture specifically within the flow component appears contradictory to the paper's own argument that complex architectures might not be necessary for effective time series representation learning, and the authors should provide more compelling theoretical or empirical justification for this architectural choice.\n2. While the paper claims computational efficiency as a major advantage, it would be significantly better to provide comprehensive analysis of the actual time costs for the proposed method compared to baseline methods.\n3. The paper fails to adequately explain how the dimensionality of the latent space is determined and whether this dimensionality choice has any principled relationship to the forecast horizon length.", "was_revised": true, "final_justification": "no more questions", "rebuttal": "Thank you for your thoughtful feedback and recognition of our work. We address your concerns below:\n\n**1.Choice of integrating Transformer into flow while adopting simple MLP encoder/decoder:**\n\nWe introduced Transformers specifically in the flow module (TarFlow) rather than the temporal encoder module **to enhance the distribution fitting capabilities**, not to learn complex temporal representations. **We posit that the enhanced posterior distribution approximation enriches the latent space's informational capacity, forming the foundation for improved generation quality, and the powerful distribution transformations performed by TarFlow allows a lightweight encoder.** Therefore, as noted by Reviewer QEJx, we intentionally used a simple MLP backbone to **isolate the contribution of our generative framework and avoid confounding effects from other complex modules**. This design clearly demonstrates the efficacy of our core method. This choice is also inspired by recent works [1,2] suggesting that simple architectures might suffice for learning time series.\n\n**2.Computational efficiency:**\n\nTable 4 empirically compares TARFVAE's inference speed (wall-clock inference time) with generative baselines. Its one-step generation significantly accelerates inference. TARFVAE maintains O(N²) complexity—matching iTransformer and DUET—thus achieving efficiency comparable to these deterministic models.\n\n**3.Latent space dimensionality:**\n\nThe latent space dimensionality is treated as a hyperparameter and selected via grid search like other hyperparameters. Theoretically, larger dimensions increase the latent space's informational capacity and may improve generation quality. However, this simultaneously requires the encoder and decoder to enhance their capacity to encode and discriminate latent variables —undoubtedly demanding greater model capacity, more data, and computational resources. Thus, dimensionality selection should balance task complexity, data volume, and computational constraints.\n\n**4.Scaling with lookback/horizon:**\n\nWe have reported the model’s performance across datasets as the forecast horizon varies from 96 to 720 in the main results table (**Table 1**), and we illustrate the average performance on each dataset for various forecast horizons while the lookback window is progressively increased from 48 to 336 in **Figure 3**. Overall, as the lookback window lengthens and the forecast horizon shortens, the forecasting task becomes easier and model accuracy improves—consistent with intuition. These results also demonstrate that TARFVAE consistently achieves superior performance compared to baselines across varying lookback windows and forecast horizons.\n\n**5.Alternatives of MLP backbone:**\n\nIn response to your interest, **we replace the MLP backbone used in our original experiments with iTransformer** and conduct a quick evaluation on the ETTm and Exchange datasets; the results are reported below. The alternative model delivers performance comparable to the original, still outperforming the other baselines in most cases. Specifically, it enjoys an edge over the original model when the horizon is short (e.g. on ETTm1 and Exchange at horizons of 96 and 192), whereas it falls slightly behind when the horizon is long. This nuanced difference is difficult to interpret conclusively; one plausible explanation is that iTransformer, being more complex than the MLP, induces slight overfitting on longer horizons. At minimum, **the experiment supports the claim that an elaborate backbone is not essential for these tasks: our generative framework powered by Tarflow's potent distribution transformations already suffices to achieve SOTA performance**.\n\n**Table: Results of original TARFVAE and iTransformer alternative. In comparisons between each TARFVAE and the other models, the best result is indicated in bold.**\n\n| Model |  | TARFVAE |  | TARFVAE-iTransformer|  | Other Top Performance |  |\n|:---|:---|:---|:---|:---|:---|:---|:---|\n| Metric |  | MSE | MAE | MSE | MAE | MSE | MAE |\n| ETTm1 | 96 | **0.311** | **0.351** | **0.306** | **0.350** | 0.323(TSMixer) | 0.354(DUET) |\n|  | 192 | **0.361** | **0.378** | **0.356** |**0.378** | 0.369(DUET) | 0.379(DUET) |\n|  | 336 | **0.391** | **0.401** | **0.391** | 0.404 | 0.400(PatchTST) | **0.402(DUET)** |\n|  | 720 | **0.456** | **0.435** | **0.458** | 0.441 | 0.463(DUET) | **0.437(DUET)** |\n|  | Avg | **0.380** | **0.391** | **0.378** | **0.393** | 0.390(DUET) | 0.393(DUET) |\n| ETTm2 | 96 | **0.171** | **0.249** | **0.171** | **0.252** | 0.174(DUET) | 0.255(DUET) |\n|  | 192 | **0.229** | **0.291** | **0.237** | **0.296** | 0.243(DUET) | 0.302(DUET) |\n|  | 336 | **0.293** | **0.334** | **0.301** | **0.341** | 0.304(DUET) | 0.341(DUET) |\n|  | 720 | **0.391** | **0.391** | **0.399** | **0.396** | 0.399(DUET) | 0.397(DUET) |\n|  | Avg | **0.271** | **0.316** | **0.277** | **0.321** | 0.280(DUET) | 0.324(DUET) |\n| Exchange | 96 | **0.086** | **0.204** | **0.083** | **0.202** | 0.086(DUET & iTransformer) | 0.205(DUET & PatchTST) |\n|  | 192 | **0.172** | **0.294** | **0.170** | **0.294** | 0.176(PatchTST & DLinear) | 0.299(iTransformer & PatchTST) |\n|  | 336 | 0.340 | 0.423 | 0.320 | 0.410 | **0.301(PatchTST)** | **0.397(PatchTST)** |\n|  | 720 | 0.797 | 0.678 | 0.855 | 0.691 | **0.654(TSMixer)** | **0.624(DUET)** |\n|  | Avg | 0.349 | 0.400 | 0.357 | 0.399 | **0.318(DUET)** | **0.384(DUET)** |\n\n\nReference:\n\n[1] Zeng et al. \"Are transformers effective for time series forecasting? \". AAAI 2023.\n\n[2] Sun et al. \"Simple feedfoward neural networks are almost all you need for time series forecasting\". 2025."}]

Author rebuttal:

Meta-review: The submission presents a time series generation approach highlighting generation efficiency for longer horizon. This is achieved by a one-step, concurrent VAE generation process, while from the performance part, an autoregressive normalizing flow encoder is used to lift the usual conditional Gaussian model for a more precise capture of the posterior distribution and a more informative latent code reflecting the given condition. The proposed approach has been shown to outperform prevalent existing approaches in forecasting quality and efficiency.

Reviewers and myself appreciate the investigation of this combination of models and the resulting preferred performance. The technical choices seem solid and well-motivated. Reviewers also raised some major insufficiencies, regarding which the authors also posted their responses:
* Evaluation baselines and metrics lacking generative/probabilistic versions, which are expected due to the generative nature of the proposed method. The authors provided one case in the rebuttal which seems supportive, while argued that more metrics and baselines are less ready for running a comparison. This seems a reasonable situation.
* Limited technical novelty. The work indeed closely follows the framework by Rezende et al. (ICML 2015). I suppose the effort to develop appropriate architectures and temporal structure design within this framework for improving time series generation could still be worth a contribution. (Regarding authors rebuttal, I suppose the original work by Rezende et al. also "avoids the costly bijective inversion at inference", as its generation process follows VAE but not the flow.)
* Capability to generate varying-length time series. This may be a common asking for one-step time-series generation approaches. Though it is acceptable to first focus on fixed-length generation performance, I still hope the authors could include such a demonstration.

Overall, I suppose the contribution of this paper outweighs its current limitations. I hence recommend an acceptance.
Decision: Accept (poster)