Mio Petrizzo

Abstract

Accurate forecasting of partially observed dynamical systems typically relies on strong modeling assumptions with prior knowledge of system dynamics, limiting applicability in high-uncertainty real-world applications. This study presents State-Forecasting Diffusion (SFDiff), a measurement-driven diffusion framework for probabilistic time-series forecasting that operates without explicit dynamical models or parametric priors. SFDiff is trained solely on observed measurements and performs latent state inference via score-based decomposition, enabling robust forecasting under noisy and incomplete observations. Forecasting generation incorporates a guidance mechanism inspired by recent time-series diffusion models while extending them to multidimensional and noise-corrupted measurements. SFDiff employs either a multilayer perceptron or transformer-based architecture to jointly capture temporal and cross-dimensional dependencies, with lagged representations to improve training efficiency. SFDiff is evaluated across a set of nonlinear synthetic dynamical systems and real-world datasets, including chaotic systems, high-dimensional mechanical systems, and North Atlantic hurricane trajectories. Across all synthetic systems, SFDiff consistently outperforms classical filtering approaches and autoregressive baselines in both point and probabilistic accuracy under minimal assumptions and reduced training data. On real-world hurricane forecasting tasks, SFDiff maintains high accuracy while simultaneously predicting latitude, longitude, and wind speed from limited inputs. These results demonstrate that SFDiff provides a general, assumption-light alternative for forecasting complex dynamical systems directly from measurements.