Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion ().

Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE model for representing structured diversity based on shape and time features, ensuring both probable predictions while being sharp and accurate. STRIPE is agnostic to the forecasting model, and we equip it with a diversification mechanism relying on determinantal point processes (DPP). We introduce two DPP kernels for modelling diverse trajectories in terms of shape and time, which are both differentiable and proved to be positive semi-definite. To have an explicit control on the diversity structure, we also design an iterative sampling mechanism to disentangle shape and time representations in the latent space. Experiments carried out on synthetic datasets show that STRIPE significantly outperforms baseline methods for representing diversity, while maintaining accuracy of the forecasting model. We also highlight the relevance of the iterative sampling scheme and the importance to use different criteria for measuring quality and diversity. Finally, experiments on real datasets illustrate that STRIPE is able to outperform state-of-the-art probabilistic forecasting approaches in the best sample prediction.

Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature, constrained by their constant variance assumption from the additive noise model (ANM). In this paper, we innovatively utilize the Location-Scale Noise Model (LSNM) to relax the fixed uncertainty assumption of ANM. A diffusion-based probabilistic forecasting framework, termed Non-stationary Diffusion (NsDiff), is designed based on LSNM that is capable of modeling the changing pattern of uncertainty. Specifically, NsDiff combines a denoising diffusion-based conditional generative model with a pre-trained conditional mean and variance estimator, enabling adaptive endpoint distribution modeling. Furthermore, we propose an uncertainty-aware noise schedule, which dynamically adjusts the noise levels to accurately reflect the data uncertainty at each step and integrates the time-varying variances into the diffusion process. Extensive experiments conducted on nine real-world and synthetic datasets demonstrate the superior performance of NsDiff compared to existing approaches. Code is available at https://github.com/wwy155/NsDiff.

Summary and Contributions: In this paper, the authors deal with the time-series forecasting problem, particularly focusing on the probabilistic setting where multiple future outcomes are estimated. In the introduction they clearly present the main drawbacks of methods available in the literature: deep learning-based models are accurate and can capture sharp variations w.r.t. the groundtruth, but they are not able to propose multiple and diverse outcomes for a given input time-series; probabilistic methods can effectively solve the diversity issue but lose the sharpness of the predicted outcomes, and do not have control over the diversity. The authors introduce a method, called STRIPE, to overcome these problems: they use a loss function based on determinantal point processes (DPP) which exploits two kernels (K_shape and K_time) purposefully designed for controlling the shape and temporal diversity; moreover since K_shape and K_time can not be simply added and optimized jointly, the authors introduce an iterative process to model independently the variations in shape and time. Then, they consider the DILATE quality loss and perform an ablation study of various diversity losses, and finally they perform a comparison with state-of-the-art techniques on both synthetic and real world datasets.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure.

Various probabilistic time series forecasting models have sprung up and shown remarkably good performance. However, the choice of model highly relies on the characteristics of the input time series and the fixed distribution that the model is based on. Due to the fact that the probability distributions cannot be averaged over different models straightforwardly, the current time series model ensemble methods cannot be directly applied to improve the robustness and accuracy of forecasting. To address this issue, we propose pTSE, a multi-model distribution ensemble method for probabilistic forecasting based on Hidden Markov Model (HMM). pTSE only takes off-the-shelf outputs from member models without requiring further information about each model. Besides, we provide a complete theoretical analysis of pTSE to prove that the empirical distribution of time series subject to an HMM will converge to the stationary distribution almost surely. Experiments on benchmarks show the superiority of pTSE overall member models and competitive ensemble methods.

With increasingly more computation being shifted to the edge of the network, monitoring of critical infrastructures, such as intermediate processing nodes in autonomous driving, is further complicated due to the typically resource-constrained environments. In order to reduce the resource overhead on the network link imposed by monitoring, various methods have been discussed that either follow a filtering approach for data-emitting devices or conduct dynamic sampling based on employed prediction models. Still, existing methods are mainly requiring adaptive monitoring on edge devices, which demands device reconfigurations, utilizes additional resources, and limits the sophistication of employed models. In this paper, we propose a sampling-based and cloud-located approach that internally utilizes probabilistic forecasts and hence provides means of quantifying model uncertainties, which can be used for contextualized adaptations of sampling frequencies and consequently relieves constrained network resources. We evaluate our prototype implementation for the monitoring pipeline on a publicly available streaming dataset and demonstrate its positive impact on resource efficiency in a method comparison.

Importantly, our approach does not make Here, we propose a general method for probabilistic any a-priori assumptions on the underlying distribution of time series forecasting. We combine an our data. The probabilistic output of our model is generated autoregressive recurrent neural network to model via Implicit Quantile Networks (Dabney et al., 2018) temporal dynamics with Implicit Quantile Networks (IQN) and is trained by minimizing the integrand of the to learn a large class of distributions over a Continuous Ranked Probability Score (CRPS) (Matheson & time-series target. When compared to other probabilistic Winkler, 1976).