ITCD: implicit trajectory-constrained diffusion for consistent time series imputation

Abstract

Diffusion has recently attracted attention in time series imputation for its potential to model the uncertainty that deterministic methods often fail to capture. However, diffusion-based approaches often exhibit suboptimal imputation performance, as they overlook the distribution shift introduced by padding and rely on noise-driven optimization that ignores direct supervision signals from observed values. This causes the models to train on biased samples and struggle to approximate the observations, ultimately leading to inconsistent imputations. To address these limitations, we propose the Implicit Trajectory-Constrained Diffusion network (ITCD), which employs a two-stage diffusion architecture to mitigate the distribution shift caused by padding, thereby enabling better adaptation to realistic data. It also implicitly guides the diffusion sampling along a coherent denoising trajectory through intermediate and terminal constraints that consider both distribution and numerical accuracy, thereby achieving more consistent imputations. Extensive experiments illustrate that ITCD outperforms baselines across various scenarios with an average improvement of 13%, showing that it achieves more consistent time series imputation.