Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion models often require a large number of neural function evaluations per sample in order to deliver accurate posterior samples. As a result, using diffusion models as stochastic samplers for Monte Carlo integration in Bayesian computation can be highly computationally expensive. This cost is especially high in large-scale inverse problems such as computational imaging, which rely on large neural networks that are expensive to evaluate. With Bayesian imaging problems in mind, this paper presents a Multilevel Monte Carlo strategy that significantly reduces the cost of Bayesian computation with diffusion models. This is achieved by exploiting cost-accuracy trade-offs inherent to diffusion models to carefully couple models of different levels of accuracy in a manner that significantly reduces the overall cost of the calculation, without reducing the final accuracy. The effectiveness of the proposed Multilevel Monte Carlo approach is demonstrated with three canonical computational imaging problems, where we observe a $4\times$-to-$8\times$ reduction in computational cost compared to conventional Monte Carlo averaging.

本研究解决了生成扩散模型在贝叶斯逆问题中计算成本高昂的问题。论文提出了一种多层次蒙特卡罗策略，该策略通过利用扩散模型的成本-精度权衡，显著降低了计算成本而不影响最终精度。实验结果表明，在处理计算成像等大规模逆问题时，该方法的计算成本降低了4到8倍。

通过多层次蒙特卡罗的生成扩散模型的贝叶斯计算