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

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.

Many fields rely on data collected over time, such as patient health records, environmental sensors, or financial transactions. However, this data often has gaps or is recorded at irregular intervals, which makes it difficult for computers to analyze or fill in missing values accurately. Most existing methods require this type of data to be evenly spaced and use techniques that can distort the original information when gaps are present.Our research introduces a new method to handle this challenge by using a mathematical tool (called the Lomb–Scargle periodogram) that can analyze unevenly spaced data without first filling in the gaps. We combine this tool with a modern machine learning approach called a diffusion model, which learns to “guess” the missing values in a way that matches both the original data and its hidden patterns.We tested our approach on both simulated and real-world data and found that it not only predicts missing values more accurately, but also better preserves important patterns over time. This work can help researchers and professionals in healthcare, climate science, and finance make better decisions using incomplete or irregular data.