A Mixture-Based Framework for Guiding Diffusion Models

• URL: http://arxiv.org/abs/2502.03332v1
• Date: Wed, 05 Feb 2025 16:26:06 GMT
• Title: A Mixture-Based Framework for Guiding Diffusion Models
• Authors: Yazid Janati, Badr Moufad, Mehdi Abou El Qassime, Alain Durmus, Eric Moulines, Jimmy Olsson,
• Abstract summary: Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems. This work proposes a novel mixture approximation of these intermediate distributions.
• Score: 19.83064246586143
• License:
• Abstract: Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time compute and thereby eliminating the need to retrain task-specific models on the same dataset. To approximate the posterior of a Bayesian inverse problem, a diffusion model samples from a sequence of intermediate posterior distributions, each with an intractable likelihood function. This work proposes a novel mixture approximation of these intermediate distributions. Since direct gradient-based sampling of these mixtures is infeasible due to intractable terms, we propose a practical method based on Gibbs sampling. We validate our approach through extensive experiments on image inverse problems, utilizing both pixel- and latent-space diffusion priors, as well as on source separation with an audio diffusion model. The code is available at https://www.github.com/badr-moufad/mgdm

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