Predicting extreme and rare events in complex systems remains a central scientific challenge due to their societal and economic impacts~\cite{lorenz1963deterministic}. Systems' strong sensitivity to initial conditions and the scarcity of rare-event data lead to inevitable forecast uncertainty. To better understand the mechanisms governing extremes~\cite{de2013predictability}, it is crucial to investigate how their predictability varies and what mechanisms control it. Traditional approaches based on Lyapunov exponents~\cite{oseledec1968multiplicative} or information-theoretic measures~\cite{delsole2004predictability} often assume persistent exponential error growth or require computationally costly ensemble forecasts~\cite{vela2024large}. These methods are further constrained in high-dimensional systems, where the forward operator may be unknown and state-dependent uncertainties are difficult to sample. In this work, we explore a Scientific Machine Learning (SciML) framework that utilizes diffusion-based generative models to learn the evolution of forecast probability distributions directly from data~\cite{kohl2023benchmarking}. We leverage the learned probabilistic forecasts to quantify event-dependent predictability limits in a canonical two-dimensional turbulent shear flow. This framework enables the systematic evaluation of predictability horizons, expressed in units of Lyapunov time, without requiring explicit access to the governing equations. Preliminary results suggest that predictability limits vary widely across extreme events, ranging from one to over four Lyapunov times. By combining the generative framework with multiscale spectral analysis, we investigate the structural origins of this variability. Our analysis indicates that extreme events are associated with the emergence of specific, recurrent coherent structures. The temporal persistence of these structures appear to be closely linked with differences in extreme-event predictability. This study demonstrates that SciML approaches can be used to link probabilistic forecasting with exploratory analysis of event-dependent structures in complex systems.