Sampling from score-based diffusion models incurs bias due to both time discretisation and the approximation of the score function. A common strategy for reducing this bias is to apply corrector steps based on the unadjusted Langevin algorithm (ULA) at each noise level within a predictor-corrector framework. However, ULA is itself a biased sampler, as it discretises a continuous diffusion process. In this work, we consider adjusted Langevin correctors that employ Metropolis--Hastings (MH) or Barker's accept-reject steps to correct for this bias. Since the target density ratio typically required by MH-based algorithms is unavailable, we propose methods that instead utilise the score function to compute the correct acceptance probability. We introduce the first exact method for adjusting Langevin corrections in diffusion models, based on a two-coin Bernoulli factory algorithm. We also propose an efficient approximation based on Simpson's rule that achieves accuracy of order $5/2$ in the step size at near-zero marginal cost. We demonstrate that these procedures improve sample quality on both synthetic and image datasets, yielding consistent gains in Fréchet Inception Distance (FID) on the latter.

翻译：从基于分数的扩散模型中进行采样会因时间离散化和分数函数的近似而产生偏差。减少这种偏差的常见策略是在预测-校正框架内，在每个噪声水平下应用基于未调整朗之万算法（ULA）的校正步。然而，ULA本身是有偏的采样器，因为它离散化了一个连续的扩散过程。在本工作中，我们考虑采用梅特罗波利斯-哈斯廷斯（MH）或巴克接受-拒绝步来校正这种偏差的调整朗之万校正器。由于基于MH算法通常所需的目标密度比不可用，我们提出利用分数函数来计算正确接受概率的方法。我们引入了基于双硬币伯努利工厂算法的首个精确方法来调整扩散模型中的朗之万校正。我们还提出了一种基于辛普森法则的高效近似方法，该方法在步长上实现了阶数为$5/2$的精度，且边际成本接近于零。我们证明这些过程在合成和图像数据集上提高了样本质量，并在后者上始终改善了弗雷歇初始距离（FID）。