Diffusion models have demonstrated strong performance in time series forecasting, yet often suffer from semantic misalignment between generated trajectories and conditioning covariates, especially under complex or multimodal conditions. To address this issue, we propose SemGuide, a plug-and-play, inference-time method that enhances covariate consistency in conditional diffusion models. Our approach introduces a scoring network to assess the semantic alignment between intermediate diffusion states and future covariates. These scores serve as proxy likelihoods in a stepwise importance reweighting procedure, which progressively adjusts the sampling path without altering the original training process. The method is model-agnostic and compatible with any conditional diffusion framework. Experiments on real-world forecasting tasks show consistent gains in both predictive accuracy and covariate alignment, with especially strong performance under complex conditioning scenarios.

Patch-wise Transformer based time series forecasting achieves superior accuracy. However, this superiority relies heavily on intricate model design with massive parameters, rendering both training and inference expensive, thus preventing their deployments on edge devices with limited resources and low latency requirements. In addition, existing methods often work in an autoregressive manner, which take into account only historical values, but ignore valuable, easy-to-obtain context information, such as weather forecasts, date and time of day. To contend with the two limitations, we propose LiPFormer, a novel Lightweight Patch-wise Transformer with weak data enriching. First, to simplify the Transformer backbone, LiPFormer employs a novel lightweight cross-patch attention and a linear transformation-based attention to eliminate Layer Normalization and Feed Forward Network, two heavy components in existing Transformers. Second, we propose a lightweight, weak data enriching module to provide additional, valuable weak supervision to the training. It enhances forecasting accuracy without significantly increasing model complexity as it does not involve expensive, human-labeling but using easily accessible context information. This facilitates the weak data enriching to plug-and-play on existing models. Extensive experiments on nine benchmark time series datasets demonstrate that LiPFormer outperforms state-of-the-art methods in accuracy, while significantly reducing parameter scale, training duration, and GPU memory usage. Deployment on an edge device reveals that LiPFormer takes only 1/3 inference time compared to classic Transformers. In addition, we demonstrate that the weak data enriching can integrate seamlessly into various Transformer based models to enhance their accuracy, suggesting its generality.

Due to the latest environmental concerns in keeping at bay contaminants emissions in urban areas, air pollution forecasting has been rising the forefront of all researchers around the world. When predicting pollutant concentrations, it is common to include the effects of environmental factors that influence these concentrations within an extended period, like traffic, meteorological conditions and geographical information. Most of the existing approaches exploit this information as past covariates, i.e., past exogenous variables that affected the pollutant but were not affected by it. In this paper, we present a novel forecasting methodology to predict NO$_2$ concentration via both past and future covariates. Future covariates are represented by weather forecasts and future calendar events, which are already known at prediction time. In particular, we deal with air quality observations in a city-wide network of ground monitoring stations, modeling the data structure and estimating the predictions with a Spatiotemporal Graph Neural Network (STGNN). We propose a conditioning block that embeds past and future covariates into the current observations. After extracting meaningful spatiotemporal representations, these are fused together and projected into the forecasting horizon to generate the final prediction. To the best of our knowledge, it is the first time that future covariates are included in time series predictions in a structured way. Remarkably, we find that conditioning on future weather information has a greater impact than considering past traffic conditions. We release our code implementation at https://github.com/polimi-ispl/MAGCRN.

This paper investigated the potential of a multivariate Transformer model to forecast the temporal trajectory of the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) for short (1 month) and long horizon (more than 1 month) periods at the regional level in Europe and North Africa. The input data covers the period from 2002 to 2022 and includes remote sensing and weather data for modelling FAPAR predictions. The model was evaluated using a leave one year out cross-validation and compared with the climatological benchmark. Results show that the transformer model outperforms the benchmark model for one month forecasting horizon, after which the climatological benchmark is better. The RMSE values of the transformer model ranged from 0.02 to 0.04 FAPAR units for the first 2 months of predictions. Overall, the tested Transformer model is a valid method for FAPAR forecasting, especially when combined with weather data and used for short-term predictions.

Accurate time series forecasting is a fundamental challenge in data science, as it is often affected by external covariates such as weather or human intervention, which in many applications, may be predicted with reasonable accuracy. We refer to them as predicted future covariates. However, existing methods that attempt to predict time series in an iterative manner with auto-regressive models end up with exponential error accumulations. Other strategies that consider the past and future in the encoder and decoder respectively limit themselves by dealing with the past and future data separately. To address these limitations, a novel feature representation strategy - shifting - is proposed to fuse the past data and future covariates such that their interactions can be considered. To extract complex dynamics in time series, we develop a parallel deep learning framework composed of RNN and CNN, both of which are used in a hierarchical fashion. We also utilize the skip connection technique to improve the model's performance. Extensive experiments on three datasets reveal the effectiveness of our method. Finally, we demonstrate the model interpretability using the Grad-CAM algorithm.