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SUMMARY:A Mixture-based framework for guiding Diffusion models - Alain Oli
 viero-Durmus - Ecole Polytechnique
DTSTART:20250521T140000Z
DTEND:20250521T150000Z
UID:TALK229822@talks.cam.ac.uk
CONTACT:123034
DESCRIPTION:Inverse problems—such as reconstructing images from partial 
 or noisy measurements\, or separating individual sources from mixed signal
 s—are inherently challenging due to their ill-posed nature. In such sett
 ings\, Bayesian inference\, when combined with generative modelling\, prov
 ides a systematic and principled approach. By using generative models trai
 ned on representative data distributions\, these methods incorporate meani
 ngful prior knowledge\, which can then be integrated with the likelihood f
 unction describing the observed data. This leads to a posterior distributi
 on\, whose samples represent plausible solutions that harmonize both the o
 bserved data and prior assumptions. In recent developments\, diffusion mod
 els have emerged as state-of-the-art generative models\, demonstrating exc
 eptional capabilities in image and audio generation tasks. Diffusion model
 s function by first progressively adding noise to data samples through a f
 orward diffusion process\, ultimately converting them into pure Gaussian n
 oise. The generative model is then trained to reverse this noising process
 \, effectively learning to reconstruct original data from noise. While dif
 fusion models provide powerful priors\, directly using them for inverse pr
 oblems typically requires constructing a posterior denoiser that blends th
 is learned prior with the gradient of the log-likelihood function derived 
 from the observations. However\, existing posterior sampling methods for d
 iffusion models often rely on crude approximations of the likelihood gradi
 ent and require significant heuristic tuning and adjustments specific to e
 ach task. In this talk\, I will introduce a novel principled approach spec
 ifically designed to overcome these limitations. The core contribution of 
 this approach is the construction of a mixture approximation of intermedia
 te posterior distributions defined by the diffusion model. The sampling is
  carried out sequentially via Gibbs sampling\, a Markov Chain Monte Carlo 
 method\, using a careful data augmentation scheme. Gibbs sampling is emplo
 yed here due to its simplicity and theoretical guarantees\, allowing for e
 xact conditional updates at each iteration\, thus ensuring stability and e
 fficiency. One key advantage of the presented algorithm is its flexibility
 : it adapts to varying levels of computational resources by adjusting the 
 number of Gibbs iterations. Consequently\, substantial performance gains c
 an be achieved by increasing inference-time computational effort. I will p
 resent extensive experimental results demonstrating strong empirical perfo
 rmance across ten diverse image restoration tasks\, involving both pixel-s
 pace and latent-space diffusion models\, and showcase its successful appli
 cation in musical source separation.
LOCATION:CBL Seminar Room
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