Conditioning Degenerate Diffusion Models

2026-09-03

AI Summary

本文针对条件生成模型中密度不存在或不平滑的问题，通过因果最优传输定义近似损失函数，以最小熵控制指导训练。

Abstract

Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define \emph{approximate} loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, à la Üstünel.

Problem

• conditioned generative models
• score functions
• singular diffusion coefficient
• causal optimal transport

Innovation

• causal optimal transport
• degenerate diffusion models
• predictable representation property