用能量模型控制生成，实现可控采样与组合生成。
Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo
- 通过蒸馏预训练扩散模型，学习能量函数以替代直接建模得分。
- 利用能量势场实现低温度采样和序列蒙特卡洛控制生成。
- 首次将扩散采样形式化为费曼-卡茨模型，支持组合生成与精确控制。
扩散模型可被表述为一系列基于能量的模型，其中得分对应于能量函数的负梯度。与直接学习得分不同，能量参数化具有优势：能量本身可用于蒙特卡洛采样器进行生成控制。然而，架构约束和训练不稳定性导致能量模型性能低于直接逼近得分或去噪器。本文提出一种新型能量函数训练方法，通过蒸馏预训练扩散模型，类似于得分向量场的亥姆霍兹分解。进一步地，我们展示了能量与得分之间的协同效应，将扩散采样过程视为费曼-卡茨模型，利用学习到的能量函数中的势场进行采样控制。该形式化使组合生成与低温采样成为可能，且可通过顺序蒙特卡洛实现。
原文摘要 · Abstract (English)
Diffusion models may be formulated as a time-indexed sequence of energy-based models, where the score corresponds to the negative gradient of an energy function. As opposed to learning the score directly, an energy parameterization is attractive as the energy itself can be used to control generation via Monte Carlo samplers. Architectural constraints and training instability in energy parameterized models have so far yielded inferior performance compared to directly approximating the score or denoiser. We address these deficiencies by introducing a novel training regime for the energy function through distillation of pre-trained diffusion models, resembling a Helmholtz decomposition of the score vector field. We further showcase the synergies between energy and score by casting the diffusion sampling procedure as a Feynman Kac model where sampling is controlled using potentials from the learnt energy functions. The Feynman Kac model formalism enables composition and low temperature sampling through sequential Monte Carlo.
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