ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusion

Yingda Fan; Dan Lu; Xiaowei Jia

cs.LGSep 29, 2026

ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusion

Authors: Yingda Fan, Dan Lu, Xiaowei Jia

Organizations: Department of Computer Science, University of Pittsburgh, Pittsburgh, PA, USA · Oak Ridge National Laboratory, Oak Ridge, TN, USA

Abstract

Time series modeling increasingly demands high-quality supervision, yet target observations remain scarce - exogenous inputs are broadly available, but target measurements are often unavailable due to cost, infrastructure, or accessibility constraints. Can models trained on observed locations reconstruct target time series where measurements have never been collected? We term this zero-shot time series reconstruction. A naive approach - directly mapping exogenous inputs to targets - can yield predictions at unobserved locations, but without target signals, such models fail to capture the intrinsic dynamics of the target variable, producing overly smooth outputs that underestimate extremes. This reveals systematic errors that call for explicit modeling and calibration. We propose ZeroDiff, which constructs an informed prior from exogenous variables alone, then learns to calibrate reconstruction errors through diffusion - training on observed locations and generalizing to unobserved ones. Experiments across diverse real-world datasets demonstrate significant improvements over existing approaches. Our code is available at https://github.com/YingdaFan/ZeroDiff-ICML2026.

Figures & tables

Figure 1: In the exogenous-only reconstruction the peaks are over-smoothed and no longer stand out (a) ; ZeroDiff calibrates it onto the ground truth, restoring their prominence (b) .

Figure 2: Proposed framework. The informed prior $\hat{\mathbf{Y}}=\Phi_{\psi,\omega}(\mathbf{X})$ combines moment estimation (VAE) with dynamics learning in standardized space, generalizing to unobserved locations. The diffusion process starts from $\mathcal{N}(\hat{\mathbf{Y}},\bar{\sigma}_{T}\mathbf{I})$ rather than pure noise, enabling calibration instead of generation. The estimated moments also guide optimization by weighting training locations based on their proximity to the target in moment space.

Model	Streamflow			Solar			Temp			Methane
Model	NSE $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	NSE $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	NSE $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	NSE $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$
Diffusion Baselines
CSDI ( Tashiro et al., 2021 )	$\dagger$	2.814	1.267	0.019	7.896	6.035	$\dagger$	6.883	4.525	$\dagger$	1.910	1.610
+ $f_{\omega}$	0.060	2.367	1.214	0.307	7.271	5.926	0.722	2.881	2.286	$\dagger$	1.229	1.083
SSSD ( Alcaraz & Strodthoff, 2022 )	$\dagger$	2.583	1.161	0.446	5.930	4.468	0.605	4.002	3.303	$\dagger$	0.974	0.890
+ $f_{\omega}$	0.071	2.348	1.201	0.374	6.534	4.865	0.746	2.756	2.113	$\dagger$	1.083	0.986

Table 1: Performance comparison across different datasets. Best results are in bold .

\uparrow

indicates higher is better,

\downarrow

indicates lower is better.

Figure 3: Qualitative comparison on Basin 02065500 (Year 1997, 365 days). Top row: reconstruction by each backbone dynamics model alone; bottom row: reconstruction enhanced by ZeroDiff. Blue : ground truth streamflow; red : model prediction. ZeroDiff consistently improves temporal fidelity, particularly at peak flow events.

Model	NSE $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$
Dynamics model $f_{\omega}$ only
LSTM ( Kratzert et al., 2018 )	0.481	1.679	0.725
DLinear ( Zeng et al., 2023 )	0.428	1.777	0.818
Mamba ( Gu & Dao, 2023 )	0.557	1.869	0.892
TimesNet ( Wu et al., 2023 )	0.517	1.613	0.706
ZeroDiff with $f_{\omega}$

Table 2: Effect of dynamics model architecture on CAMELS. Upper: dynamics model

f_{\omega}

with moment estimation; lower: full ZeroDiff pipeline with each

f_{\omega}

	Streamflow	Solar	Temp	Methane
Domain	Hydrology	Energy	Hydrology	Carbon Emission
Exog. Dim	33	48	8	16
Length	4745	4015	1095	4015
Test Loc.	100	30	42	30

Table 3: Dataset statistics. Each experiment masks one location and trains on the rest.

Pipeline	Solar	Temp	Streamflow	Methane
VAE + LSTM + Diffusion	0.846	0.868	0.596	0.788
LSTM + Diffusion (no VAE)	0.839	0.828	0.377	$-0.655$

Table 4: Ablation of VAE moment estimation. NSE across four datasets.

Dataset	Max/Min ratio	VAE error	Prior NSE $<$ 0	Improved
Solar	1.3 $\times$	2.0%	0	32/32
Temp	2.0 $\times$	14.1%	1	33/43
Streamflow	791 $\times$	18.9%	1	89/98
Methane	728 $\times$	9.9%	4	28/31

Table 5: Prior estimation error and diffusion recovery. Prior NSE

<

0 : locations where the deterministic prior fails. Improved : locations where diffusion increases NSE.

Dataset	$(\hat{\mu},\hat{\sigma})$ as input	$(\hat{\mu},\hat{\sigma})$ removed
Solar	0.846	0.831
Temp	0.868	0.842
Streamflow	0.596	0.551
Methane	0.788	0.731

Table 6: Providing VAE-estimated moments

(\hat{\mu},\hat{\sigma})

as input features to the denoiser. Removing this conditioning consistently degrades performance.

Locations out	Streamflow	Solar	Temp	Methane
1	0.596	0.846	0.868	0.788
5	0.551	0.843	0.875	0.735
10	0.554	0.843	0.865	0.749
20	0.550	0.847	0.855	0.609

Table 7: Multi-Target reconstruction (NSE). Each row holds out a different number of locations per fold; a single model is trained to reconstruct all held-out targets simultaneously.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Full time series reconstruction for Basin 02065500 over the entire 13-year training period (1989–2001, 4,745 days).

Dataset	Full Period	Train Period	Days	Test Loc.	Dynamic	Static	Exog.
CAMELS	1989–2009	1989–2001	4,745	100	6	27	33
Temp	2010–2012	2010–2012	1,095	42	8	0	8
Solar	1994–2007	1994–2004	4,015	30	45	3	48
Methane	2008–2018	2008–2018	4,015	30	7	9	16

Appendix

Table 8: Dataset statistics: temporal coverage, train/test splits, and exogenous variable counts. All datasets use daily resolution.

Model	#Params	$T$	$N_{s}$	Train (min)	Infer (min)	ms/sample	Total (min)
(a) Streamflow (531 locations, 33 features, 6,903 samples/split)
ZeroDiff	271 K	20	100	4.3	9.1	39.4	13.4
DiffusionTS †	2.33 M	100	1	12.1	3.0	21.4	15.1
NsDiff	270 K	20	100	16.8	9.2	39.9	26.0
CSDI	618 K	50	10	23.0	44.4	192.9	67.4
SSSD ‡	29.4 M	200	10	12.2	165.8	720.5	178.0

Appendix

Table 9: Computational efficiency of six diffusion-based imputation models across all datasets. Models are sorted by total per-fold time (ascending) within each panel. All datasets use 365-day sequences. Training uses early stopping with patience of 20 epochs. All experiments conducted on H100.

Dataset	Two-stage	Joint	$\Delta$
Solar	0.846	0.855	$+0.009$
Temp	0.868	0.886	$+0.018$
Streamflow	0.596	0.631	$+0.035$
Methane	0.788	0.758	$-0.030$

Appendix

Table 10: Two-stage training vs. joint optimization (NSE) across all four datasets.

Figure 5: Hyperparameter sensitivity of ZeroDiff across four datasets, measured by NSE. Each panel varies one factor: (a) diffusion steps

T

, (b) denoiser capacity (

d_{\mathrm{model}}

n_{\mathrm{layers}}

), (c) learning rate, and (d) exogenous fusion strategy.

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Zero-shot time series forecasting aims to predict future values for previously unseen series, requiring models to generalize temporal dynamics beyond the training distribution. While recent foundation models achieve strong in-domain performance through large-scale pretraining, their effectiveness often relies on broad data coverage and implicit pattern memorization, which can limit generalization when data are scarce or source and target domains are disjoint. In this work, we propose FSA, a feature-to-strategy framework for controlled zero-shot univariate forecasting. Instead of directly modeling raw sequences in the observation space, FSA learns a structured mapping from an interpretable feature space to an autoregressive strategy space. This design introduces explicit inductive biases that disentangle global trends, periodic components, and local temporal dynamics, enabling the model to capture transferable time-series structure with fewer data assumptions. Empirical results show that, under identical pretraining data, training protocol, and comparable parameter budgets, FSA outperforms Transformer-based architectures in our controlled zero-shot setting.

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