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Frequency-aware Generative Models for Multivariate Time Series Imputation
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Proposes FGTI, a frequency-aware diffusion model for multivariate time series imputation that conditions on high-frequency and dominant-frequency components fused with time-domain observations via cross-domain attention.
Problem
Imputing missing values in multivariate time series, where existing methods focus on trend and seasonal terms while the residual (high-frequency) term dominates imputation error.
Approach
Extracts high-frequency and dominant-frequency conditions via FFT/IFFT filters and fuses them with time-domain observations through time-frequency and attribute-frequency cross-attention inside a conditional diffusion denoiser.
Key results
- On KDD at 10% missing, FGTI achieves RMSE 0.406 and MAE 0.149, the best among 15 baselines including PriSTI (RMSE 0.472).
- Ablations on PhysioNet show removing the high-frequency filter raises MAE from 0.2856 to 0.3654, and removing the dominant-frequency filter raises RMSE from 0.5801 to 0.6540.
- FGTI attains the best CRPS across KDD, Guangzhou and PhysioNet at all missing rates and mechanisms reported in the appendix tables.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use FGTI instead of CSDI | KDD imputation · KDD 10% missing | RMSE: 0.459 -> 0.406 | Helped |
| use FGTI instead of PriSTI | KDD imputation · KDD 10% missing | MAE: 0.169 -> 0.149 | Helped |
| use FGTI instead of PriSTI | Guangzhou imputation · Guangzhou 10% missing | RMSE: 0.242 -> 0.230 | Helped |
| use FGTI instead of PriSTI | Guangzhou imputation · Guangzhou 10% missing | MAE: 0.170 -> 0.170 | No clear effect |
| use FGTI instead of CSDI | PhysioNet imputation · PhysioNet 10% missing | RMSE: 0.619 -> 0.580 | Helped |
| use FGTI instead of CSDI | PhysioNet imputation · PhysioNet 10% missing | MAE: 0.310 -> 0.286 | Helped |
| add cross-domain representation learning (ablation) | FGTI · KDD 10% missing | RMSE: 0.4210 -> 0.4057 | Helped |
| add frequency-domain conditions (ablation) | FGTI · Guangzhou 10% missing | RMSE: 0.2402 -> 0.2325 | Helped |
| add the dominant-frequency filter (ablation) | FGTI · PhysioNet 10% missing | RMSE: 0.6540 -> 0.5801 | Helped |
| add the high-frequency filter (ablation) | FGTI · PhysioNet 10% missing | RMSE: 0.7294 -> 0.5801 | Helped |
| use random ratio rather than a fixed training mask ratio (ablation) | FGTI · KDD 10% missing | RMSE: 0.4183 -> 0.4057 | Helped |
| use random missing rather than block missing training masks (ablation) | FGTI · KDD 10% missing | RMSE: 0.4187 -> 0.4057 | Helped |
Surprising findings
- Per-component STL analysis indicates that the residual term, not trend or seasonal, accounts for most imputation error on KDD.
Limitations
- Higher resource consumption than CSDI due to the frequency branches, as acknowledged in Section 4.4.
- Filter hyperparameters (cutoff F=0.3, kappa=10) are tuned empirically and may not transfer across datasets.
- Ground truth is unavailable for real missing values, so accuracy is evaluated on artificially masked observed values.
Experimental setup
Datasets: KDD Guangzhou PhysioNet
Benchmarks: KDD Guangzhou PhysioNet
Metrics: RMSE MAE CRPS AUC
Baselines: Mean BTMF TIDER BRITS TST SAITS TimesNet LaST FreTS GRIN TimeCIB GAIN
Builds on: CSDI DDPM classifier-free guidance diffusion
Closest papers by meaning
- Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification (NeurIPS 2025 · similarity 0.89)
- Discretizing Continuous Time Series for Imputation with Masked Diffusion Training (NeurIPS 2026 · similarity 0.88)
- BayOTIDE: Bayesian Online Multivariate Time Series Imputation with Functional Decomposition (ICML 2024 · similarity 0.87)
- HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputation (NeurIPS 2026 · similarity 0.87)
- S4M: S4 for multivariate time series forecasting with Missing values (ICLR 2025 · similarity 0.86)
- ProCTI: Prototype-Refined Global Conditioning for Diffusion-Based Time Series Imputation (NeurIPS 2026 · similarity 0.86)
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