Discretizing Continuous Time Series for Imputation with Masked Diffusion Training

Dongbin Kim; Seungyun Lee; Geonwoo Shin; Jaewook Lee

cs.LGAug 19, 2026

Discretizing Continuous Time Series for Imputation with Masked Diffusion Training

Authors: Dongbin Kim, Seungyun Lee, Geonwoo Shin, Jaewook Lee

Organizations: Seoul National University

Abstract

Time series imputation is a crucial area for reliable time series analysis, yet it remains challenging due to the complex temporal dynamics and noise of real-world data. Existing approaches, however, exhibit two limitations: missing and observed values are embedded within the same representation space without explicit structural separation, and continuous diffusion-based methods are trained to predict added noise rather than the original signal. To address these, we propose the Masked Diffusion Time-series Imputation Model (MDTIM), which leverages the training paradigm of masked diffusion model for imputation tasks. The MASK token is structurally orthogonal to valid observations, and the model directly predicts the original values, naturally aligning both the representation and the learning objective with the imputation task. To bridge the gap between discrete masked diffusion and the continuous, ordinal nature of time series, we further introduce Stochastic Discretization, which maps continuous values to ordinal-aware tokens while preserving continuous dynamics. Our experiments on diverse benchmarks confirm that MDTIM achieves superior robustness and scalability, consistently outperforming state-of-the-art deterministic and generative baselines across various missing scenarios.

Figures & tables

Figure 1: Imputation results of MDTIM on the ETTh dataset. Red regions indicate intervals where both channels are missing, while yellow regions represent single-channel missingness. The uncertainty (

\sigma

), derived from the output probability of MDTIM, is estimated to be higher in the red regions (information scarcity) compared to the yellow regions (richer information) .

Figure 2: Overview of the proposed Stochastic Discretization and Ordinal-Aware Soft Labeling framework. The process consists of three stages: (1) Masking Input Data , where missing values are identified; (2) Stochastic Discretization , which applies instance-adaptive normalization and injects stochastic noise $\epsilon\sim\mathcal{U}(-0.5,0.5)$ to bridge the continuous-discrete gap; and (3) Ordinal-Aware Soft Labeling , which maps continuous values to discrete tokens while generating soft target distributions to preserve ordinal semantic relationships.

Figure 3: Overview of the Masked Diffusion Time-series Imputation Model (MDTIM) framework. The architecture operates on the discretized input through three key phases: (a) Discretized Token Embedding: The discrete tokens generated by the stochastic tokenizer are mapped into dense vector representations. (b) Ordinal-Spectral Consistent Training: The backbone is trained with a dual objective combining Ordinal-Aware Soft Cross-Entropy and Spectral Consistency Loss. This ensures spectral consistency across global frequencies while maintaining local ordinal accuracy. (c) Continuous Reconstruction via Expectation: Finally, continuous values are recovered by computing the probability-weighted expectation of the predicted token distribution, enabling precise dense reconstruction from discrete outputs.

Dataset		Energy				ETTh				Weather				Sine
Missing Type		Uniform		Geometric		Uniform		Geometric		Uniform		Geometric		Uniform		Geometric
Model		30%	70%	30%	70%	30%	70%	30%	70%	30%	70%	30%	70%	30%	70%	30%	70%
RNN	BRITS	0.246	0.379	0.329	0.366	0.194	0.299	0.227	0.292	0.050	0.073	0.058	0.071	0.010	0.021	0.020	0.019
	MRNN	1.086	1.143	1.087	1.143	0.743	0.782	0.751	0.781	0.651	0.661	0.654	0.659	0.169	0.170	0.169	0.170
	GRUD	0.364	0.457	0.426	0.445	0.310	0.394	0.348	0.383	0.104	0.369	0.164	0.350	0.008	0.014	0.013	0.012
Transformer	Transformer	0.323	0.401	0.354	0.393	0.168	0.252	0.183	0.247	0.076	0.070	0.083	0.068	0.039	0.046	0.042	0.045

Table 1: Quantitative comparison of multivariate time-series imputation performance (

L=48

). We report the MAE of MDTIM and baselines averaged over 3 random seeds at missing ratios of 30% and 70% (50% in Appendix D.1 ). The best results are highlighted in bold .

Length	96						192
Missing Type	Uniform			Geometric			Uniform			Geometric
Model	30%	50%	70%	30%	50%	70%	30%	50%	70%	30%	50%	70%
BRITS	0.191	0.229	0.287	0.220	0.250	0.280	0.192	0.230	0.287	0.222	0.250	0.280
SAITS	0.139	0.162	0.204	0.150	0.172	0.200	0.145	0.162	0.198	0.156	0.171	0.195
CSDI	0.149	0.177	0.222	0.162	0.187	0.218	0.170	0.199	0.245	0.183	0.209	0.241
MDTIM	0.124	0.152	0.199	0.138	0.163	0.194	0.123	0.148	0.190	0.135	0.157	0.186

Table 2: Robustness analysis on extended sequence lengths (

L\in\{96,192\}

). We report the MAE averaged over 3 random seeds.

		Energy		ETTh		Sine
Missing Type	Rate	CSDI	MDTIM	CSDI	MDTIM	CSDI	MDTIM
Uniform	30%	0.0629	0.0429	0.1120	0.0863	0.0023	0.0020
	50%	0.0747	0.0541	0.1356	0.1078	0.0025	0.0020
	70%	0.0927	0.0771	0.1748	0.1520	0.0030	0.0020
Geometric	30%	0.0732	0.0547	0.1262	0.1017	0.0027	0.0020
	50%	0.0818	0.0626	0.1460	0.1197	0.0028	0.0020

Table 3: Quantitative comparison of probabilistic imputation performance (CRPS,

L=48

). We compare MDTIM with the diffusion-based baseline CSDI. Lower is better.

PhysioNet2012	Uniform			Geometric
Model	30%	50%	70%	30%	50%	70%
BRITS	0.333	0.364	0.408	0.356	0.379	0.405
SAITS	0.283	0.314	0.360	0.298	0.324	0.358
CSDI	0.303	0.332	0.376	0.320	0.342	0.374
ImputeFormer	0.289	0.329	0.389	0.311	0.343	0.388
FGTI	0.338	0.376	0.425	0.370	0.397	0.423

Table 4: Imputation performance on PhysioNet 2012.

Scale	Small					Large
Model	30%	50%	70%	Params (M)	Time (s)	30%	50%	70%	Params (M)	Time (s)
BRITS	0.246	0.296	0.379	2.18	4.88	0.245	0.293	0.371	8.55	4.96
SAITS	0.212	0.216	0.240	25.25	0.41	0.177	0.185	0.212	88.24	0.79
CSDI	0.094	0.112	0.139	1.19	401.69	0.074	0.093	0.128	4.49	894.76
MDTIM (Ours)	0.046	0.065	0.092	0.65	4.05	0.044	0.061	0.085	8.33	12.63

Table 5: Imputation performance and efficiency on Energy (uniform missing). Inference time is measured on the full test set (MDTIM:

M{=}10

noise samples; CSDI:

T{=}50

diffusion steps).

Energy	Forecast Horizon
Imputer	$H{=}4$	$H{=}6$	$H{=}8$	$H{=}12$
SAITS	0.187	0.207	0.224	0.254
CSDI	0.171	0.190	0.208	0.237
MDTIM (Ours)	0.138	0.153	0.170	0.200

Table 6: Forecasting MAE on Energy (

L{=}48

) using a fixed PatchTST predictor with imputed inputs from each model.

Components		ETTh			Energy			Sine
Exp. Unmasking	Soft-Label	30%	50%	70%	30%	50%	70%	30%	50%	70%
✗	✗	0.134	0.166	0.229	0.053	0.073	0.101	0.0071	0.0072	0.0075
✗	✓	0.131	0.162	0.222	0.056	0.079	0.115	0.0069	0.0070	0.0074
✓	✗	0.129	0.159	0.212	0.044	0.060	0.085	0.0026	0.0030	0.0036
✓	✓	0.127	0.157	0.211	0.044	0.061	0.085	0.0022	0.0026	0.0035

Table 7: Ablation study on unmasking and labeling strategies. All results are reported as MAE averaged over 3 random seeds under the uniform missing scenario.

ETTh	Uniform			Geometric
Bins	30%	50%	70%	30%	50%	70%
20	0.138	0.166	0.217	0.157	0.181	0.211
40	0.127	0.157	0.211	0.146	0.173	0.205
60	0.129	0.160	0.214	0.148	0.175	0.208

Table 8: MAE on ETTh with varying vocabulary size (

K

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Datasets	Features	Frequency	Samples	Domain
Energy	28	10 min.	19,735	Weather
ETTh	7	60 min.	17,420	Temperature
Weather	21	10 min.	52,696	Weather
Sine	5	-	10000	Simulation

Appendix

Table 9: Statistics of benchmark datasets.

Category	Parameter	Value	Description
Model	Hidden Size ( $D$ )	256	Dimension of hidden states
	Attention Heads	16	Number of heads in MSA
	DiT Blocks ( $L$ )	5	Number of factorized layers
	Dropout	0.2	Dropout probability
	Bins ( $K$ )	40	Vocabulary size for discretization
	Output Range	1.5	Value range $[-1.5,1.5]$

Appendix

Table 10: Hyperparameters for MDTIM architecture and training.

Dataset		Energy						ETTh						Weather						Sine
Missing Type		Uniform			Geometric			Uniform			Geometric			Uniform			Geometric			Uniform			Geometric
Model		30%	50%	70%	30%	50%	70%	30%	50%	70%	30%	50%	70%	30%	50%	70%	30%	50%	70%	30%	50%	70%	30%	50%	70%
RNN	BRITS	0.246	0.296	0.379	0.329	0.344	0.366	0.194	0.235	0.299	0.227	0.258	0.292	0.050	0.057	0.073	0.058	0.063	0.071	0.010	0.013	0.021	0.020	0.019	0.019
	MRNN	1.086	1.107	1.143	1.087	1.108	1.143	0.743	0.762	0.782	0.751	0.765	0.781	0.651	0.653	0.661	0.654	0.656	0.659	0.169	0.169	0.170	0.169	0.169	0.170
	GRUD	0.364	0.387	0.457	0.426	0.425	0.445	0.310	0.336	0.394	0.348	0.362	0.383	0.104	0.176	0.369	0.164	0.231	0.350	0.008	0.008	0.014	0.013	0.012	0.012
Transformer	Transformer	0.323	0.335	0.401	0.354	0.356	0.393	0.168	0.201	0.252	0.183	0.212	0.247	0.076	0.067	0.070	0.083	0.072	0.068	0.039	0.041	0.046	0.042	0.044	0.045

Appendix

Table 11: Quantitative comparison of multivariate time-series imputation performance (

L=48

). We report the MAE of MDTIM and baselines averaged over 3 random seeds. The best results are highlighted in bold .

Panel of Figure 4 — Figure 4: Comparison between MDTIM (Disc) and MDTIM (Cont) on the Energy dataset, alongside representative baselines (SAITS, CSDI). Results are reported under both uniform and geometric missing scenarios across varying missing rates.

Panel of Figure 5 — Figure 5: Visualization of imputation results on the ETTh dataset.

Panel of Figure 6 — Figure 6: Visualization of imputation results on the Energy dataset.

Panel of Figure 7 — Figure 7: Visualization of imputation results on the Weather dataset.

Panel of Figure 8 — Figure 8: Visualization of imputation results on the Sine dataset.

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