Bayesian computation with generative diffusion models by Multilevel Monte Carlo.

Area of Science:

• Computational mathematics
• Machine learning
• Scientific imaging

Background:

• Generative diffusion models offer accurate solutions for Bayesian inverse problems.
• Diffusion models require numerous function evaluations, leading to high computational costs for Monte Carlo integration and uncertainty quantification.
• Large-scale problems like computational imaging exacerbate these costs due to expensive neural network evaluations.

Purpose of the Study:

• To present a novel Multilevel Monte Carlo (MLMC) strategy to reduce the computational cost of Bayesian computation using diffusion models.
• To address the high computational expense associated with diffusion model sampling in inverse problems, particularly in quantitative imaging.

Main Methods:

• Developed a Multilevel Monte Carlo strategy tailored for diffusion models.
• Exploited inherent cost-accuracy trade-offs within diffusion models.
• Coupled diffusion models of varying accuracy levels to minimize overall computational cost.

Main Results:

• Achieved a significant reduction in computational cost for Bayesian computation with diffusion models.
• Demonstrated a [Formula: see text]-to-[Formula: see text] cost reduction compared to standard techniques across three benchmark imaging problems.
• Maintained final accuracy while substantially decreasing computational demands.

Conclusions:

• The proposed MLMC strategy effectively reduces the computational burden of using diffusion models for Bayesian inverse problems.
• This approach offers a computationally efficient solution for uncertainty quantification in large-scale applications like computational imaging.
• The method enables more feasible application of diffusion models in demanding scientific domains.