Abstract
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 a distributional tail scoring rule to construct differentiable tail-aware objectives. We prove that the population loss uniquely identifies the intended tail law, quantify its finite implementation gap, and bound the terminal sampler perturbation by the accumulated realised guidance updates. On synthetic data, TailDiff approaches the empirical lower bound. On a challenging financial tail-risk simulation benchmark, it outperforms the state-of-the-art on tail metrics while preserving bulk structure.
Shuning Zhao (赵舒宁）
Ph.D. Candidate - Department of Computer Science and Technology, Tsinghua University
My research interests include the application of Artificial Intelligence and Machine Learning in Finance, Insurance, Speech, and Audio domains.
Patrick Wong
Lecturer (Assistant Professor) - Department of Econometrics and Business Statistics, Monash University
My research focuses on actuarial science, financial mathematics, AI, Machine Learning and commodity market dynamics, including the evaluation and valuation of variable annuities in general stochastic environments, jump-diffusion processes in crude oil markets, and higher-order risk-neutral moments.
Xiaolin Hu
Professor - Department of Computer Science and Technology, Tsinghua University
Faculty member of Department of Computer Science and Technology, Tsinghua University, working in the TSAIL group directed by Prof. Bo Zhang and Prof. Jun Zhu. My current research interests include artificial neural networks and computational neuroscience. I’m an Associate Editor of IEEE Transactions on Pattern Analysis and Machine Intelligence, IEEE Transactions on Image Processing and Cognitive Neurodynamics. Previously I was an Associate Editor of IEEE Transactions on Neural Networks and Learning Systems. I’m a Senior Member of IEEE.