Discretizing Continuous Time Series for Imputation with Masked Diffusion Training

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

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.

When Denoising Hurts: Rethinking the Terminal Step of Diffusion Time Series Forecasters -- Extended Version

Diffusion models offer a natural way to model uncertainty in time series forecasting, yet their iterative sampling process is often treated as a uniformly beneficial refinement procedure. Our study challenges this view by examining how forecast quality evolves throughout reverse diffusion. We find that general temporal structure is often recovered at relatively high noise levels, whereas continued low-noise refinement can introduce statistical drift and degrade the final forecast. Our analysis further suggests that this behavior explains why prior methods often favor relatively narrow diffusion architecture and schedule design. Building on this observation, we propose a label-free global stopping criterion that detects the optimal termination point, eventually speeding up inference and improving predictive accuracy. Additionally, since early stopping terminates inference in high-noise regions, we propose a Bernoulli timestep sampler that concentrates training on this region while preserving coverage of the full diffusion process. Extensive experiments conducted across eight real-world datasets demonstrate the superior performance of our method compared to existing approaches.

TS-MTM: Temporal-Spectral Masked Time-Series Modeling for Forecasting

Time series forecasting is a cornerstone of numerous real-world applications, where prediction accuracy relies on capturing intricate periodic patterns and evolving spectral dynamics. While Masked Time-series Modeling (MTM) has emerged as a powerful self-supervised paradigm, its conventional one-dimensional (1D) formulation often fails to resolve the underlying structural dependencies essential for long-term forecasting explicitly. To address this limitation, we propose TS-MTM, a Temporal-Spectral Masked Time-series Modeling framework that formalizes pretraining within a joint representation space. By leveraging autocorrelation-based periodicity, TS-MTM transforms 1D sequences into period-aware 2D temporal-spectral representations, a transition grounded in stochastic-process theory. Within this augmented space, we introduce two synergistic mechanisms: Axial-Period Cross Masking (APCM) to capture temporal dependencies across phases, and Structure-aware Spectral Magnitude Masking (SSMM) to reconstruct global frequency-domain signatures. To ensure representation consistency, a Dual-domain Contextual Contrastive objective is employed to align these complementary views on the signal manifold, yielding unified embeddings that preserve temporal-spectral coherence. Extensive evaluations across nine benchmark datasets demonstrate that TS-MTM consistently achieves state-of-the-art performance under both in-domain and cross-domain settings, underscoring its robustness and generalization for complex temporal dynamics. Code is available at https://github.com/zpc2002zpc/TS-MTM.

Pseudotime-conditioned diffusion models for imputing time-series single-cell data

Probabilistic diffusion-based imputation methods have demonstrated superior performance over many state-of-the-art approaches for imputing single-cell data. However, existing methods typically rely on isotropic Gaussian noise and canonical observation time, limiting their ability to capture structured temporal dependencies and continuous cellular dynamics. In time-series single-cell RNA-seq (scRNA-seq) data, these limitations are exacerbated by the small number of experimentally measured time points and the substantial heterogeneity among cells collected at the same time point, causing observed time labels to poorly reflect true biological progression. To address these challenges, we propose the first pseudotime-conditioned diffusion-based imputation framework for time-series scRNA-seq data, consisting of two trajectory-aware models: pseudotime-conditioned conditional score-based diffusion imputation (P-CSDI) and pseudotime-conditioned hybrid-noise CSDI (PH-CSDI). P-CSDI incorporates inferred pseudotime as a conditioning signal to guide the denoising process with biologically meaningful temporal structure, while PH-CSDI further introduces hybrid structured noise to improve frequency-aware temporal modeling. By leveraging pseudotime as a continuous representation of cellular progression, both models enable trajectory-aware and temporally coherent reconstruction of missing gene expression values. P-CSDI and PH-CSDI consistently reduce mean absolute error (MAE) and root mean squared error (RMSE) by approximately 40%–60% compared with state-of-the-art imputation methods across two scRNA-seq datasets under diverse missingness settings. These findings highlight the importance of incorporating biologically informed temporal structure into diffusion-based generative models for accurate imputation of dynamic single-cell transcriptomic data. The computer code and data for the proposed method are available on GitHub: https://github.com/gbishop345/pseudotime-CSDI.

Nonparametric generative modeling for time series via Schr¨odinger bridge

StrideDiffusion: Accelerating Diffusion Models for Time-series Generation

Diffusion models have become competitive generators for time series, but their practical use is limited by the large number of sequential denoising steps required at inference time. Existing fast samplers typically use fixed or generic timestep schedules, overlooking a distinctive property of time-series diffusion: different spectral bands evolve at different rates during the reverse process. We introduce StrideDiffusion, a training-free spectral-aware sampler that adaptively selects the denoising stride from band-level activity. At each step, StrideDiffusion monitors relative band energy, log-power drift, and phase velocity to identify whether high- frequency dynamics remain active or whether the trajectory is dominated by stable low-frequency structure. It then takes fine steps when rapidly varying bands are active and larger jumps once only coarse components remain. A bandwise stability analysis shows that inactive frequency bands change only linearly with the jump size under deterministic affine reverse updates, providing a local justification for spectral activity as a step-size indicator. Across six unconditional time-series generation benchmarks, StrideDiffusion uses only 14-66 function evaluations instead of 500/1000 denoising steps, achieving up to 18.9x wall-clock speedup while preserving or improving generation quality. On conditional imputation and forecasting, it further delivers 5-14x average acceleration with comparable predictive accuracy. These results show that spectral evolution provides a practical and principled signal for fast time-series diffusion sampling. Our code is available at https://anonymous.4open.science/r/stridediff-ts.