Conditional sampling within generative diffusion models.

Area of Science:

• Machine Learning
• Computational Statistics
• Bayesian Inference

Background:

• Generative diffusion models are powerful Monte Carlo samplers for high-dimensional distributions.
• Current limitations exist in applying these models to conditional sampling tasks, crucial for Bayesian inverse problems.

Purpose of the Study:

• To provide a comprehensive review of computational approaches for conditional sampling in generative diffusion models.
• To highlight methodologies for constructing conditional generative samplers.

Main Methods:

• Reviewing techniques that leverage the joint distribution for conditional sampling.
• Examining methods that utilize pre-trained marginal distributions with explicit likelihoods.
• Focusing on computational approaches within generative diffusion models.

Main Results:

• Identified key methodologies for conditional sampling in generative diffusion models.
• Categorized approaches based on the use of joint or marginal distributions.
• Highlighted the importance of explicit likelihoods in certain marginal distribution methods.

Conclusions:

• Conditional sampling in generative diffusion models is an active research area with various computational strategies.
• The reviewed methods offer pathways to apply diffusion models to conditional tasks, including Bayesian inverse problems.
• Further development in this area promises advancements in generative modeling for complex scientific challenges.