Diffusion models can be parameterised in terms of either a score or an energy function. An energy parameterisation is appealing since it enables an extended sampling procedure with a Metropolis--Hastings (MH) correction step, based on the change in total energy in the proposed samples. Improved sampling is important for model compositions, where off-the-shelf models are combined with each other, in order to sample from new distributions. For model composition, score-based diffusions have the advantages that they are popular and that many pre-trained models are readily available. However, this parameterisation does not, in general, define an energy, and the MH acceptance probability is therefore unavailable, and generally ill-defined. We propose keeping the score parameterisation and computing an acceptance probability inspired by energy-based models through line integration of the score function. This allows us to reuse existing diffusion models and still combine the reverse process with various Markov-Chain Monte Carlo (MCMC) methods. We evaluate our method using numerical experiments and find that score-parameterised versions of the MCMC samplers can achieve similar improvements to the corresponding energy parameterisation.

翻译：扩散模型既可以用分数函数参数化，也可以用能量函数参数化。能量参数化具有吸引力，因为它能够基于所提样本总能量的变化，通过Metropolis-Hastings（MH）修正步骤实现扩展采样过程。改进采样对于模型组合至关重要，其中现成模型相互结合以从新分布中采样。对于模型组合，基于分数的扩散模型具有两大优势：其应用广泛且许多预训练模型易于获取。然而，这种参数化通常不定义能量函数，因此MH接受概率无法获得且通常定义不明确。我们提出保持分数参数化，并通过分数函数的线积分计算受能量模型启发的接受概率。这使得我们能够重用现有扩散模型，并将逆向过程与各种马尔可夫链蒙特卡洛（MCMC）方法相结合。我们通过数值实验评估所提方法，发现MCMC采样器的分数参数化版本能够实现与相应能量参数化类似的改进效果。