MCMC Correction of Score-Based Diffusion Models for Model Composition.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Statistics

Background:

• Diffusion models can be parameterized by score or energy functions.
• Energy-based diffusion models facilitate Markov Chain Monte Carlo (MCMC) sampling with Metropolis-Hastings (MH) corrections for improved sample quality, especially in model composition.
• Score-based diffusion models are prevalent but lack inherent energy functions, precluding MH-based sampling.

Purpose of the Study:

• To enable Metropolis-Hastings (MH)-like sampling for score-based diffusion models.
• To allow the integration of existing score-based diffusion models with MCMC techniques.
• To improve sample quality in diffusion model composition without explicit energy parameterization.

Main Methods:

• Developed a novel Metropolis-Hastings (MH)-like acceptance rule based on line integration of the score function.
• Retained score parameterization for diffusion models.
• Integrated the novel acceptance rule with annealed MCMC techniques.

Main Results:

• The proposed MH-like samplers achieve significant improvements in sampling quality.
• The method yields relative improvements comparable to energy-based models.
• Demonstrated effectiveness on both synthetic and real-world datasets.

Conclusions:

• The novel MH-like acceptance rule effectively bridges score-based diffusion models and MCMC sampling.
• This approach allows leveraging existing diffusion models for enhanced sampling quality.
• The method offers a viable alternative for model composition without explicit energy functions.