Blue Noise-based Generative Models for the Imputation of Time-series Data

Reconstructing missing data in high-dimensional time-series remains a challenging task, especially when the underlying signals exhibit complex temporal dynamics and non-linear relationships. While most traditional approaches can not model such intricacies, generative models-particularly conditional score-based diffusion methods-have emerged as powerful alternatives, offering significant improvements in imputation accuracy. Despite their success, these models typically rely on isotropic white noise during training, which treats all frequency components uniformly and fails to preserve critical frequency-dependent correlations. Relying solely on white noise can lead to the loss of fine-scale temporal patterns, compromising the accuracy and reliability of the reconstructed data. Our recent work introduces a time-varying blue noise-based conditional score-based diffusion model for imputation (tBN-CSDI) by incorporating a time-varying blue noise schedule into the diffusion process to address the limitations of existing methods in handling missing values in time series data. Experimental results on real-world datasets demonstrate that tBN-CSDI outperforms conventional methods based on white noise schedules. We also discuss the integration of pseudotime analysis with diffusion models as a promising direction for future research, particularly for applications in dynamic biological systems where temporal ordering is critical yet uncertain.