A Mixture-Based Framework for Guiding Diffusion Models

Yazid Janati, Badr Moufad, Mehdi Abou El Qassime, Alain Oliviero Durmus, Eric Moulines, Jimmy Olsson
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:26830-26876, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-janati25a, title = {A Mixture-Based Framework for Guiding Diffusion Models}, author = {Janati, Yazid and Moufad, Badr and Qassime, Mehdi Abou El and Oliviero Durmus, Alain and Moulines, Eric and Olsson, Jimmy}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {26830--26876}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/janati25a/janati25a.pdf}, url = {https://proceedings.mlr.press/v267/janati25a.html}, 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.} }
Endnote
%0 Conference Paper %T A Mixture-Based Framework for Guiding Diffusion Models %A Yazid Janati %A Badr Moufad %A Mehdi Abou El Qassime %A Alain Oliviero Durmus %A Eric Moulines %A Jimmy Olsson %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-janati25a %I PMLR %P 26830--26876 %U https://proceedings.mlr.press/v267/janati25a.html %V 267 %X 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.
APA
Janati, Y., Moufad, B., Qassime, M.A.E., Oliviero Durmus, A., Moulines, E. & Olsson, J.. (2025). A Mixture-Based Framework for Guiding Diffusion Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:26830-26876 Available from https://proceedings.mlr.press/v267/janati25a.html.

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