TailDiff: Elicitable Tail-Guided Diffusion for Risk-Sensitive Generation

Generative models are increasingly used to simulate risk-sensitive systems, from financial markets and energy demand to healthcare, where downstream decisions depend on rare but consequential events. In this setting, matching average behavior is not enough: rare tail events drive stress testing, capital allocation, and policy analysis. Yet tail objectives such as Value-at-Risk and Expected Shortfall are difficult to optimize directly because empirical estimators rely on sorting, thresholding, and subset selection. We introduce TailDiff, a training-free inference-time guidance method for pretrained diffusion models that uses jointly elicitable Fissler-Ziegel scoring rules to construct differentiable tail-aware objectives. We analyze the induced guidance field locally in the low-noise regime, characterizing tail-shaping and boundary-coupling behavior together with controlled perturbations under small realized effective drift. On synthetic data, TailDiff approaches the oracle finite-sample floor, on a challenging financial tail-risk simulation benchmark, it outperforms the state-of-the-art on tail metrics while preserving bulk structure.