NASDiff: Noise-Aware Diffusion With Short-Trajectory Learning for Consistent Time Series Imputation

Abstract

Diffusion models have attracted growing interest in time series imputation for their ability to model uncertainty beyond deterministic methods. However, existing diffusion-based approaches often overlook the impact of distinct noise sources on learning. Specifically, padding-induced noise introduces spurious values that lead to distributional shifts, while diffusion-added noise obscures representative variations captured by high-frequency components, jointly resulting in inconsistent imputation. Meanwhile, their probabilistic denoising paradigm relies on step-by-step reverse diffusion process that traverses the full reverse trajectory, leading to inefficient sampling. To address both issues, we propose Noise-Aware Diffusion with Short-trajectory learning for consistent time series imputation (NASDiff). Specifically, NASDiff builds a noise-aware diffusion framework that explicitly models distinct noise sources. It integrates multi-scale frequency decomposition to mitigate padding-induced distortion, and adopts a low-frequency-oriented diffusion process to decouple diffusion-added noise from intrinsic high-frequency component, thereby enabling more consistent imputation. Moreover, we propose a short-trajectory learning strategy for diffusion-based imputation that models the implicit reverse process on shortened, non-consecutive trajectories, enabling efficient sampling. Extensive experiments on seven real-world datasets show that NASDiff consistently outperforms baselines across point, subsequence and block missing scenarios, yielding an average 14.15% improvement in imputation accuracy while substantially reducing diffusion sampling time.