TLDR: This survey paper explores the application of diffusion models, originally known for image synthesis, to time series forecasting (TSF). It details how these generative models are adapted to predict future time series values by learning from historical and multimodal data. The paper categorizes existing approaches based on their conditioning sources (historical time series, multimodal data) and how these conditions are integrated (feature-centric vs. diffusion-centric). It also reviews common datasets and evaluation metrics, discusses current limitations such as slow inference and lack of standardization, and proposes future research directions, including foundation models and adaptive architectures, to advance the field.
Time series forecasting (TSF) is a crucial task across many fields, from predicting energy demand and traffic flow to monitoring healthcare trends. Traditionally, TSF has evolved from statistical models like ARIMA to advanced deep learning methods such as recurrent neural networks (RNNs), convolutional neural networks (CNNs), and Transformers. Recently, generative models, particularly diffusion models, have gained significant attention for their ability to capture uncertainty and produce high-quality forecasts.
What are Diffusion Models?
Diffusion models, initially developed for generating realistic images, are a type of generative model that learns complex data distributions through a two-step process: progressive noising and reverse denoising. In the context of TSF, these models are adapted to generate future sequences based on past observations and other relevant information. During training, Gaussian noise is gradually added to the actual future sequence. A neural network, guided by historical context, then learns to reverse this noising process. When making predictions, the model starts with noise and iteratively refines it into a forecast, effectively sampling from the learned probability distribution of future outcomes.
Advantages in Time Series Forecasting
Diffusion models offer several key benefits for TSF. Firstly, they can produce probabilistic forecasts, which means they don’t just give a single prediction but a range of possible future scenarios, allowing for better uncertainty quantification. Secondly, they are known for their stable training behavior, avoiding the common instability issues seen in other generative models like Generative Adversarial Networks (GANs). Lastly, their flexible generative capabilities allow for seamless integration of various conditioning signals, such as additional variables or multimodal inputs.
How Diffusion Models are Adapted for TSF
The core idea is to use diffusion models as conditional generative models, where the goal is to generate future sequences conditioned on past observations. The historical time series typically serves as the primary conditioning input. The model learns to reconstruct future values from noise, guided by this historical context. For a deeper dive into the technical details, you can refer to the full research paper: Diffusion Models for Time Series Forecasting: A Survey.
Conditioning Information: The Key to Better Forecasts
The effectiveness of diffusion models in TSF heavily relies on the quality and type of conditioning information provided. Researchers have explored two main categories:
Historical Time Series Conditions
Many approaches use the raw historical time series directly. However, more sophisticated methods extract richer temporal information. This includes decomposing the series into components like trend, seasonality, and residuals, or analyzing it at multiple scales to capture different temporal dynamics. Some models even use frequency-domain transformations (like Fourier decomposition) to provide complementary perspectives. Novel techniques also involve retrieval augmentation, where similar historical segments are used as references, or transforming time series into compressed latent representations to extract salient features efficiently.
Multimodal Data Conditions
Beyond just time series data, incorporating multimodal information can provide richer context. For example, some models convert time series into multi-view images or generate textual descriptions based on statistical features, using these as additional conditions. Other approaches integrate external data, such as news articles published concurrently with the time series, to capture external influences that might not be present in the numerical data alone.
Integrating Conditions into the Diffusion Process
How conditioning information is integrated is as important as its source. Two main strategies exist:
Feature-centric Approaches
These methods use a standard diffusion model but focus on designing a powerful feature extractor for the historical data. The extracted features then guide each denoising step, ensuring the generated sequence is consistent with its past. Examples include using recurrent neural networks (RNNs) or Transformer-based networks to capture temporal dependencies. Some innovative approaches also incorporate mechanisms like ‘future mixup’ (blending historical projection with ground-truth future) or ‘brain-inspired memories’ to enrich the conditioning signal.
Diffusion-centric Approaches
These approaches modify the diffusion process itself. One direction involves integrating time series-specific priors into the forward noising process, making the noise addition procedure more tailored to time series data. This prior information also guides the reverse denoising. Another direction replaces the standard noise addition with alternative processes, such as deterministic interpolation or Brownian Bridge diffusion, to better capture the inherent characteristics and reduce uncertainty in TSF tasks.
Datasets and Evaluation
Diffusion-based TSF models are evaluated using various datasets, broadly categorized into unimodal (pure temporal signals like Exchange Rates, Weather, Electricity, Traffic) and multimodal (time series combined with text or images, such as Time-MMD or TTC). Performance is assessed using both deterministic metrics (like Mean Squared Error – MSE, and Mean Absolute Error – MAE) and probabilistic metrics (like Continuous Ranked Probability Score – CRPS), which evaluate how well the predicted distribution aligns with actual observations.
Also Read:
- Rethinking Time-Series Forecasting: The Power of Learnable Dynamics
- A New Approach to Understanding Time Series Signals: Focusing on Structure Over Amplitude
Current Limitations and Future Outlook
Despite significant progress, diffusion-based TSF faces challenges. Time series data itself can be complex, exhibiting non-stationarity, abrupt shifts, and long-term dependencies that are hard to capture. Current diffusion models often suffer from slow inference speeds due to their iterative nature and may not fully leverage the potential of rich multimodal data. Interpretability remains a challenge due to the use of high-dimensional latent spaces. Furthermore, a lack of standardized evaluation protocols across studies hinders fair comparisons and reproducibility.
Looking ahead, promising research directions include developing general-purpose ‘foundation models’ for time series that can generalize across diverse domains with minimal training. Designing adaptive architectures that automatically adjust forecasting parameters based on input characteristics is another key area. Finally, improving long-term multivariate forecasting by mitigating error accumulation and effectively incorporating auxiliary multimodal priors will be crucial for real-world applications in complex domains like energy management and climate prediction.
