Diachronic Sample Integration: Robust Tail-Risk Estimation with Generative Models

2026-07-12

AI Summary

This work addresses the challenge that deep generative models struggle to stably estimate low-probability tail events in risk-sensitive scenarios, as their training objectives prioritize overall distributional fidelity over extreme outcomes. To mitigate this limitation without altering the generative objective, the authors propose a test-time inference framework that constructs a mixture distribution by aggregating samples from multiple checkpoints along the training trajectory, thereby smoothing tail fluctuations. This approach—novel in leveraging temporal training dynamics for tail estimation—combines diffusion models with distribution mixing and includes a theoretical bias-variance analysis. Empirical results demonstrate that, under limited simulation budgets, the method significantly reduces tail estimation error compared to single-checkpoint sampling and existing tail-aware baselines across both synthetic high-dimensional and real-world high-frequency trading datasets.

Abstract

Deep generative models are increasingly used as simulators for downstream decision-making under data scarcity, but in risk-sensitive applications their usefulness depends on rare adverse scenarios rather than typical samples. Standard generative objectives prioritize bulk distributional fidelity, leaving low-probability tails vulnerable to localized optimization noise and making tail-dependent functionals unstable under finite simulation budgets. We introduce Diachronic Sample Integration (DSI), a test-time inference framework that ensembles generated samples across checkpoints from a stochastic training trajectory. DSI targets a checkpoint-mixture distribution that averages checkpoint-specific tail fluctuations rather than relying on a single brittle endpoint. We formalize this mechanism through a finite-budget bias-variance theory. Empirically, across multivariate synthetic processes and high-frequency trading data, DSI substantially reduces tail-estimation error compared to single-checkpoint baselines under fixed simulation budgets, outperforming standard diffusion and state-of-the-art tail-aware baselines without modifying the generative objective.

Problem

• tail-risk estimation
• generative models
• data scarcity
• distributional tails
• simulation budget

Innovation

• Diachronic Sample Integration
• tail-risk estimation
• generative models
• checkpoint ensemble
• bias-variance tradeoff