Diffusion models can be parameterised in terms of either a score or an energy function. The energy parameterisation has better theoretical properties, mainly that it enables an extended sampling procedure with a Metropolis--Hastings correction step, based on the change in total energy in the proposed samples. However, it seems to yield slightly worse performance, and more importantly, due to the widespread popularity of score-based diffusion, there are limited availability of off-the-shelf pre-trained energy-based ones. This limitation undermines the purpose of model composition, which aims to combine pre-trained models to sample from new distributions. Our proposal, however, suggests retaining the score parameterization and instead computing the energy-based acceptance probability through line integration of the score function. This allows us to re-use existing diffusion models and still combine the reverse process with various Markov-Chain Monte Carlo (MCMC) methods. We evaluate our method on a 2D experiment and find that it achieve similar or arguably better performance than the energy parameterisation.

翻译：扩散模型可基于得分函数或能量函数进行参数化。能量参数化具有更优的理论特性，主要在于它能通过提议样本总能量变化的Metropolis-Hastings校正步骤实现扩展采样过程。然而，这种参数化方法似乎会略降低性能，且更关键的是，由于基于得分的扩散模型普遍流行，现成的预训练能量模型资源十分有限。这一局限性削弱了模型组合（即结合预训练模型从新分布中采样）的目标价值。然而，我们的方案主张保留得分参数化方式，转而通过得分函数的线积分计算基于能量的接受概率。这使得我们既能复用现有扩散模型，又能将逆向过程与各类马尔可夫链蒙特卡洛（MCMC）方法相结合。我们在2D实验上评估了该方法，发现其能达到与能量参数化相当或更优的性能。