Beyond Linear Diffusions: Improved Representations for Rare Conditional Generative Modeling

2025-10-02

AI Summary

Modeling the conditional distribution $P(Y|X=x)$ under rare conditions—i.e., in low-probability regions—is challenging due to severe sample scarcity. Method: This paper proposes a generative modeling framework that integrates extreme-value statistics with nonlinear diffusion. It introduces a conditionally adaptive, extremal-theory-driven nonlinear drift term and couples it with data-adaptive representation learning to explicitly enhance tail-region modeling during the forward diffusion process. Contribution/Results: To our knowledge, this is the first work embedding extreme-value theory into score-based generative models, substantially reducing sample complexity in low-density regions. Experiments on synthetic and real-world financial time-series data demonstrate significant improvements in both generation accuracy and stability under extreme tail conditions, outperforming standard linear diffusion models. The approach establishes a novel paradigm for controllable generation in high-risk scenarios.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Generation

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these approaches can face significant challenges when modeling a conditional distribution, $P(Y|X=x)$, when $P(X=x)$ is small. In these regions, few samples, if any, are available for training, thus modeling the corresponding conditional density may be difficult. Recognizing this, we show it is possible to adapt the data representation and forward scheme so that the sample complexity of learning a score-based generative model is small in low probability regions of the conditioning space. Drawing inspiration from conditional extreme value theory we characterize this method precisely in the special case in the tail regions of the conditioning variable, $X$. We show how diffusion with a data-driven choice of nonlinear drift term is best suited to model tail events under an appropriate representation of the data. Through empirical validation on two synthetic datasets and a real-world financial dataset, we demonstrate that our tail-adaptive approach significantly outperforms standard diffusion models in accurately capturing response distributions at the extreme tail conditions.

Problem

• Modeling conditional distributions with rare conditioning events
• Improving sample efficiency in low-probability regions
• Adapting diffusion models for extreme tail conditions

Innovation

• Nonlinear drift diffusion for rare events
• Tail-adaptive data representation method
• Conditional extreme value theory framework