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SimDiff: Simpler Yet Better Diffusion Model for Time Series Point Forecasting

Hang Ding, Xue Wang, Tian Zhou, Tao Yao

TL;DR

SimDiff addresses the gap between probabilistic diffusion models and accurate point forecasting in time series by proposing a simple, end-to-end diffusion framework. It integrates a unified Transformer denoiser/predictor, Normalization Independence to handle distribution drift, and a Median-of-Means ensemble to convert samples into precise point estimates, achieving state-of-the-art MSE on multiple datasets while maintaining competitive probabilistic metrics. The approach yields faster inference than prior diffusion models due to its single-stage design and RoPE-enhanced temporal modeling. These contributions offer a practical, scalable pathway to reliable point forecasts in real-world, non-stationary time series scenarios.

Abstract

Diffusion models have recently shown promise in time series forecasting, particularly for probabilistic predictions. However, they often fail to achieve state-of-the-art point estimation performance compared to regression-based methods. This limitation stems from difficulties in providing sufficient contextual bias to track distribution shifts and in balancing output diversity with the stability and precision required for point forecasts. Existing diffusion-based approaches mainly focus on full-distribution modeling under probabilistic frameworks, often with likelihood maximization objectives, while paying little attention to dedicated strategies for high-accuracy point estimation. Moreover, other existing point prediction diffusion methods frequently rely on pre-trained or jointly trained mature models for contextual bias, sacrificing the generative flexibility of diffusion models. To address these challenges, we propose SimDiff, a single-stage, end-to-end framework. SimDiff employs a single unified Transformer network carefully tailored to serve as both denoiser and predictor, eliminating the need for external pre-trained or jointly trained regressors. It achieves state-of-the-art point estimation performance by leveraging intrinsic output diversity and improving mean squared error accuracy through multiple inference ensembling. Key innovations, including normalization independence and the median-of-means estimator, further enhance adaptability and stability. Extensive experiments demonstrate that SimDiff significantly outperforms existing methods in time series point forecasting.

SimDiff: Simpler Yet Better Diffusion Model for Time Series Point Forecasting

TL;DR

SimDiff addresses the gap between probabilistic diffusion models and accurate point forecasting in time series by proposing a simple, end-to-end diffusion framework. It integrates a unified Transformer denoiser/predictor, Normalization Independence to handle distribution drift, and a Median-of-Means ensemble to convert samples into precise point estimates, achieving state-of-the-art MSE on multiple datasets while maintaining competitive probabilistic metrics. The approach yields faster inference than prior diffusion models due to its single-stage design and RoPE-enhanced temporal modeling. These contributions offer a practical, scalable pathway to reliable point forecasts in real-world, non-stationary time series scenarios.

Abstract

Diffusion models have recently shown promise in time series forecasting, particularly for probabilistic predictions. However, they often fail to achieve state-of-the-art point estimation performance compared to regression-based methods. This limitation stems from difficulties in providing sufficient contextual bias to track distribution shifts and in balancing output diversity with the stability and precision required for point forecasts. Existing diffusion-based approaches mainly focus on full-distribution modeling under probabilistic frameworks, often with likelihood maximization objectives, while paying little attention to dedicated strategies for high-accuracy point estimation. Moreover, other existing point prediction diffusion methods frequently rely on pre-trained or jointly trained mature models for contextual bias, sacrificing the generative flexibility of diffusion models. To address these challenges, we propose SimDiff, a single-stage, end-to-end framework. SimDiff employs a single unified Transformer network carefully tailored to serve as both denoiser and predictor, eliminating the need for external pre-trained or jointly trained regressors. It achieves state-of-the-art point estimation performance by leveraging intrinsic output diversity and improving mean squared error accuracy through multiple inference ensembling. Key innovations, including normalization independence and the median-of-means estimator, further enhance adaptability and stability. Extensive experiments demonstrate that SimDiff significantly outperforms existing methods in time series point forecasting.

Paper Structure

This paper contains 32 sections, 35 equations, 9 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. SimDiff: Simpler yet Better Diffusion Model
  3. Diffusion and Denoising For Time Series
  4. Normalization Independence
  5. Transformer Denoising Network
  6. Median of Means Ensemble
  7. Loss Function for Robust Training
  8. Experiments
  9. Probabilistic Forecasting Underpins Accurate Point Estimates
  10. Accurate Long-Term Time Series Point Forecasting
  11. Standard Diffusion Transformer Suffices for Accurate Point Forecasting
  12. Significance of Training-Specific Normalization Independence
  13. Ensemble Enhances SimDiff as an Effective Point Estimator
  14. Inference Efficiency
  15. Related Works
  16. ...and 17 more sections

Figures (9)

  • Figure 1: Trustworthy Forecasting by Ensembling Diverse Probability Samples
  • Figure 2: Visualizations on ETTh1 by (a) CSDI, (b) TimeDiff, and (c) SimDiff. CSDI only shows 90% interval due to the existence of extreme samples.
  • Figure 3: SimDiff: We have developed a streamlined end-to-end patch-based transformer diffusion model for time series forecasting tasks. Key components of our design include Normalization Independence, MoM ensembling, and the incorporation of RoPE.
  • Figure 4: Normalization Independence: Enhancing Robust Training by Mitigating O.O.D.
  • Figure 5: The MoM Ensemble
  • ...and 4 more figures