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LSCD: Lomb--Scargle Conditioned Diffusion for Time series Imputation

ICML 2025 · Time series › Causal and generative time series · approach: Irregular series and imputation · 0 citations (OpenAlex)

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Proposes LSCD, a score-based diffusion model for time series imputation conditioned on a differentiable Lomb-Scargle periodogram spectrum (plus a spectral consistency loss), evaluated on synthetic sines and PhysioNet/PM2.5.

Problem

Time series with missing or irregularly sampled values break FFT-based frequency analysis, which needs uniform sampling and pre-interpolation that distorts spectra; imputation methods typically ignore spectral consistency.

Approach

Compute a differentiable Lomb-Scargle periodogram directly from observed (irregular, masked) values, filter it by false alarm probability, encode it with an attention-based spectrum encoder to condition a CSDI-style conditional diffusion model at every denoising step, and add a spectral consistency loss on the reconstructed series during a final fine-tuning stage.

Key results

• On Physionet at 10% missing, LSCD reaches MAE 0.211 and RMSE 0.494 versus CSDI's 0.219 and 0.545.
• On Sines (MCAR 50%), LSCD reduces S-MAE to 0.014 versus 0.027 for CSDI, the strongest baseline on spectral error.
• On PM2.5 (10% missing), LSCD gets MAE 9.069 versus 9.670 for CSDI and S-MAE 0.022 versus 0.023.

Measured effects reported in the paper

Surprising findings

• At 90% missingness on Physionet, the reported S-MAE of LSCD (0.093) ties CSDI, so gains in spectral error largely vanish at high missingness.
• The ablation shows removing the Lomb-Scargle conditioning has only small effects on MAE (0.219 vs 0.211 at 10% missing), suggesting modest contributions per component.

Limitations

• The grid-based diffusion architecture needs interpolation time points known at training time, unlike continuous-time methods.
• The Lomb-Scargle periodogram assumes sinusoidal structure, and the spectral consistency loss can bias the model away from the score-matching optimum.
• Physionet S-MAE gains vanish at 90% missingness, and the PM2.5 missingness is partly artificial.

Experimental setup

Datasets: Synthetic Sines PhysioNet PM2.5 Beijing air quality

Benchmarks: Synthetic Sines PhysioNet PM2.5

Metrics: MAE RMSE S-MAE CRPS

Baselines: Mean Lerp BRITS GPVAE US-GAN TimesNet SAITS CSDI ModernTCN

Builds on: CSDI Lomb-Scargle periodogram score-based diffusion models

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