LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputation

TL;DR

This paper introduces LSCD, a novel diffusion-based method utilizing a differentiable Lomb-Scargle layer for accurate time series imputation of irregularly sampled data, outperforming time-domain methods and enabling spectral guidance.

Contribution

The paper presents a differentiable Lomb-Scargle layer integrated into a score-based diffusion model for improved time series imputation with irregular sampling.

Findings

Outperforms time-domain baselines in missing data recovery

Provides consistent frequency spectrum estimates

Easily integrates into existing learning frameworks

Abstract

Time series with missing or irregularly sampled data are a persistent challenge in machine learning. Many methods operate on the frequency-domain, relying on the Fast Fourier Transform (FFT) which assumes uniform sampling, therefore requiring prior interpolation that can distort the spectra. To address this limitation, we introduce a differentiable Lomb--Scargle layer that enables a reliable computation of the power spectrum of irregularly sampled data. We integrate this layer into a novel score-based diffusion model (LSCD) for time series imputation conditioned on the entire signal spectrum. Experiments on synthetic and real-world benchmarks demonstrate that our method recovers missing data more accurately than purely time-domain baselines, while simultaneously producing consistent frequency estimates. Crucially, our method can be easily integrated into learning frameworks, enabling broader adoption of spectral guidance in machine learning approaches involving incomplete or irregular data.