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Divide-and-conquer posterior sampling for denoising diffusion priors
Janati, Yazid Moufad, Badr Durmus, Alain Moulines, Eric Olsson, Jimmy
Janati, Yazid
Moufad, Badr
Durmus, Alain
Moulines, Eric
Olsson, Jimmy
Supervisor
Department
Machine Learning
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Conference proceeding
Date
2024
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Language
English
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Abstract
Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors.Although these have great potential, DDM priors yield complex posterior distributions that are challenging to sample from.Existing approaches to posterior sampling in this context address this problem either by retraining model-specific components, leading to stiff and cumbersome methods, or by introducing approximations with uncontrolled errors that affect the accuracy of the produced samples.We present an innovative framework, divide-and-conquer posterior sampling, which leverages the inherent structure of DDMs to construct a sequence of intermediate posteriors that guide the produced samples to the target posterior.Our method significantly reduces the approximation error associated with current techniques without the need for retraining.We demonstrate the versatility and effectiveness of our approach for a wide range of Bayesian inverse problems.The code is available at \url{https://github.com/Badr-MOUFAD/dcps}
Citation
Y. Janati, B. Moufad, A. Durmus, E. Moulines, and J. Olsson, “Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors,” Adv Neural Inf Process Syst, vol. 37, pp. 97408–97444, Dec. 2024, Accessed: Mar. 25, 2025. [Online]. Available: https://github.com/Badr-MOUFAD/dcps
Source
Advances in Neural Information Processing Systems (NeurIPS 2024)
Conference
Keywords
Local identifiability, Deep ReLU neural networks, Parameter recovery, Geometric conditions, Finite sample analysis?
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Publisher
NEURIPS