提出RNE框架，统一实现扩散模型的推理时控制与能量训练
RNE: plug-and-play diffusion inference-time control and energy-based training
- 基于密度比理论，通过反向路径推导生成过程中的边缘分布
- 在推理时控制任务中表现优异，支持退火与模型组合，扩展性强
- 适用于连续与离散扩散模型，可直接嵌入现有框架
扩散模型通过逐步去噪生成数据，对应于加噪过程的时间反演。然而，仅依赖去噪核常不足以满足实际需求。许多应用需要生成轨迹中各阶段的边缘密度信息，以支持推理时控制等任务。为此，本文提出径度尼姆估计器（RNE），基于路径分布之间的密度比概念，揭示了边缘密度与转移核间的根本联系。RNE构建了一个灵活的即插即用框架，统一实现了（1）扩散密度估计、（2）推理时控制、（3）基于能量的扩散训练。实验表明，RNE在推理时控制任务（如退火与模型组合）中表现强劲，具备良好的推理时扩展性；同时为基于能量的扩散模型训练提供了简单高效的正则化方法。此外，所提RNE具有模态无关性，既适用于连续扩散模型，也适用于其离散版本。
原文摘要 · Abstract (English)
Diffusion models generate data by removing noise gradually, which corresponds to the time-reversal of a noising process. However, access to only the denoising kernels is often insufficient. In many applications, we need the knowledge of the marginal densities along the generation trajectory, which enables tasks such as inference-time control. To address this gap, in this paper, we introduce the Radon-Nikodym Estimator (RNE). Based on the concept of the \textit{density ratio} between path distributions, it reveals a fundamental connection between marginal densities and transition kernels, providing a flexible plug-and-play framework that unifies (1) diffusion density estimation, (2) inference-time control, and (3) energy-based diffusion training under a single perspective. Experiments demonstrate that RNE delivers strong results in inference-time control applications, such as annealing and model composition, with promising inference-time scaling performance, and achieves a simple yet efficient regularisation for training energy-based diffusion models. Additionally, our proposed RNE is modality-agnostic and applicable not only to continuous diffusion models but also to their discrete diffusion counterparts.
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