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.

FastDiSS: Few-step Match Many-step Diffusion Language Model on Sequence-to-Sequence Generation--Full Version

Self-conditioning has been central to the success of continuous diffusion language models, as it allows models to correct previous errors. Yet its ability degrades precisely in the regime where diffusion is most attractive for deployment: few-step sampling for fast inference. In this study, we show that when models only have a few denoising steps, inaccurate self-conditioning induces a substantial approximation gap; this mistake compounds across denoising steps and ultimately dominate the sample quality. To address this, we propose a novel training framework that handles these errors during learning by perturbing the self-conditioning signal to match inference noise, improving robustness to prior estimation errors. In addition, we introduce a token-level noise-awareness mechanism that prevents training from saturation, hence improving optimization. Extensive experiments across conditional generation benchmarks demonstrate that our framework surpasses standard continuous diffusion models while providing up to 400x faster inference speed, and remains competitive against other one-step diffusion frameworks.