LSCD · Lomb–Scargle Conditioned Diffusion for Time Series Imputation

Abstract

Time series imputation with missing or irregularly sampled data is a persistent challenge in machine learning. Most frequency-domain methods rely on the Fast Fourier Transform (FFT), which assumes uniform sampling, therefore requiring interpolation or imputation prior to frequency estimation. We propose a novel diffusion-based imputation approach (LSCD) that leverages Lomb–Scargle periodograms to robustly handle missing and irregular samples without requiring interpolation or imputation in the frequency domain. Our method trains a score-based diffusion model conditioned on the entire signal spectrum, enabling direct usage of irregularly spaced observations. 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 framework paves the way for broader adoption of Lomb–Scargle methods in machine learning tasks involving irregular data.

Lomb-Scargle

FFT vs Lomb-Scargle: FFT assumes uniform sampling, requiring interpolation when missing or irregularly sampled data is present. Lomb-Scargle operates on irregular data directly, avoiding interpolation and providing a more accurate frequency estimate.

Model Architecture

Lomb-Scargle Spectrum: Quick Start

pip install git+https://github.com/asztr/LombScargle.git

import torch
import math
import LombScargle

# Define example time series with single frequency = 5
t = torch.linspace(0, 10.0, 200) #timestamps
y = torch.sin(2*math.pi*5.0*t) #values

# Select frequencies to evaluate
freqs = torch.linspace(1e-5, 10.0, 100)

# Compute the normalized spectrum
ls = LombScargle.LombScargle(freqs)
P = ls(t, y, fap=True, norm=True)  # [1, 100] array of power values

BibTeX

@inproceedings{lscd2025,
  title     = {LSCD: Lomb–Scargle Conditioned Diffusion for Time-Series Imputation},
  author    = {Elizabeth Fons and Alejandro Sztrajman and Yousef El-Laham and Luciana Ferrer and
               Svitlana Vyetrenko and Manuela Veloso},
  booktitle = {Proc. 42nd International Conference on Machine Learning},
  year      = {2025}
}