ProCTI: Prototype-Refined Global Conditioning for Diffusion-Based Time Series Imputation

Fariza Rashid; Duc Van Le; Rahat Masood; Gustavo Batista; Aruna Seneviratne; Suranga Seneviratne

cs.LGSep 29, 2026

ProCTI: Prototype-Refined Global Conditioning for Diffusion-Based Time Series Imputation

Authors: Fariza Rashid, Duc Van Le, Rahat Masood, Gustavo Batista, Aruna Seneviratne, Suranga Seneviratne

Organizations: University of Sydney · University of New South Wales

Abstract

Time series imputation has progressed from statistical and deep learning approaches to diffusion-based models, which have shown strong recent performance. Existing diffusion-based methods typically condition the reverse process using local contextual information from the current or neighbouring windows. Meanwhile, global dataset-level structure often remains implicit, limiting performance when local observations are sparse, noisy, or unrepresentative. To address this issue, we propose ProCTI, a diffusion-imputation framework that augments local conditioning with retrieved global dataset-level priors through learned prototypes. A hybrid conditioning mechanism integrates this global context with local signals during reverse diffusion, enabling more accurate reconstruction under varying missingness scenarios. Experiments across multiple benchmark datasets show that ProCTI outperforms strong baselines overall under random missingness, while remaining competitive under attribute-wise missingness. Furthermore, we use a latent-regime data model to characterise the precise conditions under which prototype-derived global conditioning provably improves imputation. We support this with a general theoretical analysis of local-global conditioning.

Figures & tables

Panel of Figure 1 — Figure 1 : Regime structure and representative imputation behaviour in the Beijing dataset. (a) UMAP projection of normalised windows after PCA, coloured by K-means derived regimes. (b) Mean feature profiles of the discovered regimes, showing distinct combinations of pollution and meteorological conditions. (c) Example masked-window reconstruction for NO2, where ProCTI better matches the ground truth than competing baselines.

Figure 2 : Prototype-conditioning module

Panel of Figure 3 — Figure 3 : Feature correlation heatmaps for the five datasets: (a) PhysioNet, (b) Weather, (c) Stock, (d) Gait, and (e) Beijing.

Variant	Proto Bank	Proto Attn	Learnable $\boldsymbol{\alpha}$	Gait		PhysioNet		Weather		Beijing		Stock
Variant	Proto Bank	Proto Attn	Learnable $\boldsymbol{\alpha}$	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE
A	–	–	–	0.322	0.531	0.228	0.460	0.149	0.336	0.1566	0.4338	3.2606	4.0410
B	✓	–	–	0.318	0.521	0.219	0.424	0.113	0.296	0.1518	0.4062	2.6317	3.2982
C	✓	✓	–	0.317	0.520	0.217	0.417	0.119	0.304	0.1519	0.4044	2.4705	3.0971
D	frozen	✓	–	0.316	0.521	0.221	0.434	0.139	0.329	0.1591	0.4362	2.9831	3.7186
E (inj-dom)	✓	✓	✓	0.316	0.518	0.219	0.414	0.096	0.280	0.1515	0.4043	2.2686	2.8323

Table 3 : Ablation study of ProCTI across all datasets (mean values only). Variant A denotes the base FGTI model without prototype conditioning. Variants B–D use fixed

\alpha=0.1

, while Variant E uses a learnable

\alpha

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Metric	Missing	CSDI	Diffusion-TS	FGTI	PaD-TS	MTSCI	ProCTI
CRPS $(\downarrow)$	0.10	0.1798	0.6579	0.1187	0.8727	0.4076	0.1286
	0.30	0.1867	0.8361	0.1362	0.8955	0.5980	0.1390
	0.50	0.2223	0.8485	0.1647	1.0370	0.6081	0.1593
	0.70	0.2284	0.7599	0.2266	0.9718	0.7307	0.2040
PI90 Coverage $(~90\%)$	0.10	0.8447	0.0368	0.8479	0.1383	0.8053	0.8467
	0.30	0.8460	0.0514	0.9097	0.2291	0.7806	0.8876

Appendix

Table 4 : Probabilistic evaluation on the test split across missingness ratios on PhysioNet data.

Metric	Missing	CSDI	Diffusion-TS	FGTI	MTSCI	PaD-TS	ProCTI
CRPS $(\downarrow)$	0.10	0.1646	0.2368	0.1204	0.2286	0.6141	0.1185
	0.30	0.1700	0.2326	0.1282	0.2374	0.5920	0.1254
	0.50	0.1894	0.2393	0.1472	0.2639	0.5784	0.1424
	0.70	0.2119	0.2400	0.1679	0.2861	0.5657	0.1617
PI90 Coverage $(~90\%)$	0.10	0.8439	0.3016	0.8152	0.7506	0.1611	0.8536
	0.30	0.8479	0.3478	0.8279	0.7657	0.2946	0.8748

Appendix

Table 5 : Probabilistic evaluation on the test split across missingness ratios on Beijing data.

Figure 4 : Runtime and peak GPU memory usage for different models on the Beijing dataset under the 30% missingness test setting.

Metric	Prototype bank size	Beijing	Gait	PhysioNet	Stock	Weather
MAE	16	0.200	0.310	0.222	0.894	0.102
	32	0.158	0.310	0.224	0.835	0.118
	64	0.202	0.306	0.216	1.030	0.095
RMSE	16	0.481	0.519	0.416	1.187	0.450
	32	0.412	0.510	0.438	1.118	0.387
	64	0.482	0.512	0.413	1.340	0.434

Appendix

Table 6 : Effect of prototype bank size (number of prototypes) on imputation performance. Best results for each dataset and metric are highlighted in bold.

Figure 5 : Effect of scaling parameter

\alpha\in\{0.1,0.3\}

on imputation performance. Lower values indicate better imputation performance.

Dataset	$r$	Metric	$t$ -stat	$t$ -test $p$	Wilcoxon stat	Wilcoxon $p$
Beijing	0.1	MAE	-0.306	0.388	5	0.313
	0.1	RMSE	-2.590	0.030	1	0.063
	0.3	MAE	-3.111	0.018	0	0.031
	0.3	RMSE	-2.156	0.049	2	0.094
	0.5	MAE	-1.950	0.062	1	0.063
	0.5	RMSE	-2.677	0.028	1	0.063

Appendix

Table 8 : Paired one-sided significance tests for ProCTI vs. FGTI across 5 seeds (

H_{1}

: ProCTI error

<

FGTI error).

p

-values below 0.05 are in bold. With

n=5

, the minimum attainable Wilcoxon

p

-value is

1/32\approx 0.031

Dataset	$n_{\text{active}}$ (threshold)	$n_{\text{active}}$ (90% cumulative)
Stock	31	27
Weather	32	29
PhysioNet	32	29
Beijing	32	29
Gait	32	28

Appendix

Table 9 : Number of active prototypes per dataset under the usage threshold and the 90% cumulative usage criterion.

Panel of Figure 6 — Figure 6 : Representative imputation comparison on the Beijing dataset.

Panel of Figure 7 — Figure 7 : Representative imputation comparison on the Gait dataset.

Panel of Figure 8 — Figure 8 : Representative imputation comparison on the PhysioNet dataset.

Panel of Figure 9 — Figure 9 : Prototype usage visualisation examples on the Stock dataset for four representative windows. Each panel shows (a) the raw time-series window, (b) prototype attention weights, (c) the residual regime vector $r_{b}$ , and (d)–(f) the dominant-frequency signal before and after prototype-based adjustment for the three channels with the largest $|r_{b}|$ . The prototype attention weights and $r_{b}$ values are obtained after training for 50 epochs, at which point the learned scaling parameter is $\alpha=0.0907$ .

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Multivariate time series imputation (MTSI) aims to recover missing values in temporal data composed of multiple interdependent variables. This problem is central to real-world applications such as healthcare monitoring, traffic networks, and energy systems. Recent diffusion-based approaches have shown strong potential for probabilistic imputation by learning to generate missing values through iterative denoising. However, most existing approaches perform diffusion directly in the original data space, requiring the denoising network to simultaneously capture global structure, temporal dynamics, and stochastic variability. This makes the generative task unnecessarily complex, especially when modern deterministic imputers can already provide accurate initial reconstructions. To address this limitation, we propose RDDMPI, a conditional residual diffusion framework that operates directly in residual space. Instead of modeling the full missing signal directly, we reformulate probabilistic imputation as a baseline-residual decomposition, where a pretrained model captures the dominant signal and a diffusion process models the residual uncertainty. To better exploit deterministic guidance, \model{} conditions the reverse denoising process on both the baseline-completed signal and its latent representation, while a reliability-aware conditioning mechanism adaptively controls the influence of baseline information during residual generation. This formulation simplifies the diffusion learning objective, enabling it to focus on structured correction terms rather than reconstructing the full signal. Experiments on multiple benchmark datasets demonstrate that RDDMPI consistently improves both reconstruction accuracy and uncertainty quantification.

Abstract

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