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.

通过对评分函数进行线积分计算来计算基于能量的接受概率，从而实现扩展的采样过程，使我们能够重复使用现有的扩散模型并将其与各种马尔科夫链蒙特卡洛方法结合。我们在一个二维实验中评估了我们的方法，并发现其达到了与能量参数化方法相似或更好的性能。

基于评分的扩散模型修正的MCMC方法用于模型组合