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HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputation

NeurIPS 2026 · Time series › Causal and generative time series · approach: Diffusion models for time series · 0 citations (OpenAlex)

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Proposes HyFAD, a coupled time-frequency DDPM-style diffusion model with a frequency-aware step embedding for time series imputation, reporting state-of-the-art MAE/RMSE on PhysioNet and Air Quality.

Problem

Existing diffusion models for time series imputation inject and denoise noise only in the time domain, which underweights high-frequency details, balances global trends and local dynamics poorly, and use frequency-agnostic step embeddings.

Approach

Coupled forward/reverse diffusion where frequency-domain noise is injected before time-domain noise (and removed in mirrored order), with a frequency-aware step embedding that gates sinusoidal step features by noise-aware, stage-aware and missing-aware band weights.

Key results

• On PhysioNet 10%/50%/90% missingness, HyFAD reaches MAE 0.206/0.288/0.448 and RMSE 0.423/0.622/0.782, the best among compared methods.
• On Air Quality, HyFAD achieves MAE 9.296 and RMSE 17.730, versus 9.340/18.270 for the second-best LSCD.
• Replacing the frequency-aware embedding with the standard diffusion embedding raises PhysioNet 10% RMSE from 0.423 to 0.439 (ablation at same settings).

Surprising findings

• Setting lambda=0.25 (frequency-dominant noise allocation) degrades performance substantially, indicating time-domain noise should carry most of the noise budget.

Limitations

• Frequency exploration limited to DFT (rDFT); other transforms such as DCT or DWT not studied.
• Uses DDIM deterministic sampling; probabilistic imputation and DDPM sampling not evaluated.
• Frequency-domain sampling can be less numerically stable than time-domain sampling.

Experimental setup

Datasets: PhysioNet Air Quality

Benchmarks: PhysioNet Air Quality

Metrics: MAE RMSE

Baselines: Mean Lerp BRITS GP-VAE SSGAN TimesNet CSDI SAITS ModernTCN LSCD

Builds on: CSDI DDPM DDIM FourierDiffusion

Closest papers by meaning

• LSCD: Lomb--Scargle Conditioned Diffusion for Time series Imputation (ICML 2025 · similarity 0.89)
• Discretizing Continuous Time Series for Imputation with Masked Diffusion Training (NeurIPS 2026 · similarity 0.89)
• Time Series Diffusion in the Frequency Domain (ICML 2024 · similarity 0.88)
• Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification (NeurIPS 2025 · similarity 0.88)
• Frequency-aware Generative Models for Multivariate Time Series Imputation (NeurIPS 2024 · similarity 0.87)
• Efficient Denoising Diffusion via Probabilistic Masking (ICML 2024 · similarity 0.87)