DREA: A Probabilistic Distributional Attribution Framework for Trustworthy Explanations in Diffusion-Based Predictive Models

Abstract Diffusion-based generative models can produce predictive distributions, but their explanations are often derived from point-attribution methods that do not quantify how predictors influence uncertainty, distributional shape, or extreme-event behavior. We propose Distributional Reliability Explanation Attribution (DREA), a probabilistic attribution framework for diffusion-based predictive models. Instead of assigning a single importance score, DREA estimates how reliably predictor perturbations alter properties of generated predictive distributions across repeated bootstrap realizations. The framework decomposes attribution into distributional shift, uncertainty width, variance, tail-risk behavior, and probabilistic skill using empirical reliability frequencies. We validate DREA with a controlled synthetic benchmark in which separate predictors control the conditional mean, predictive variance, upper-tail behavior, correlated proxy information, and irrelevant noise. DREA recovers the known distributional roles: mean drivers are identified through distributional-shift and skill components, uncertainty drivers through width and variance components, and tail drivers through tail-risk components. This decomposition shows not only which predictors matter, but which aspect of the predictive distribution they control. DREA also assigns near-zero reliability to irrelevant noise and lower reliability to the Mean-proxy variable than to the true Mean driver. We further demonstrate DREA on diffusion-based hydrological forecasting using streamflow, meteorological, and basin predictors. The real-world experiment shows that DREA decomposes predictor influence into interpretable probabilistic components associated with predictive skill, uncertainty amplification, variance control, and upper-tail discharge risk. Event-level analyses provide local explanations by estimating how often predictor perturbations change predicted discharge and flood-tail probability. DREA extends explainability from point-wise feature importance to probabilistic distributional attribution for uncertainty-sensitive decision support.