Variational Diffusion Posterior Sampling with Midpoint Guidance.
Badr Moufad (PhD student, Ecole Polytechnique)
| When |
Apr 15, 2025
from 01:00 to 02:00 |
|---|---|
| Where | M7 101 |
| Attendees |
Badr Moufad |
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Badr MOufad
Title: Variational Diffusion Posterior Sampling with Midpoint Guidance.
Abstract: Diffusion models have recently shown considerable potential in solving Bayesian
inverse problems when used as priors. However, sampling from the resulting denoising pos-
terior distributions remains a challenge as it involves intractable terms. To tackle this issue,
state-of-the-art approaches formulate the problem as that of sampling from a surrogate dif-
fusion model targeting the posterior and decompose its scores into two terms: the prior score
and an intractable guidance term. While the former is replaced by the pre-trained score of
the considered diffusion model, the guidance term has to be estimated. In this paper, we
propose a novel approach that utilises a decomposition of the transitions which, in contrast
to previous methods, allows a trade-off between the complexity of the intractable guidance
term and that of the prior transitions. We validate the proposed approach through extensive
experiments on linear and nonlinear inverse problems, including challenging cases with latent
diffusion models as priors. We then demonstrate its applicability to various modalities and
its promising impact on public health by tackling cardiovascular disease diagnosis through
the reconstruction of incomplete electrocardiograms.
inverse problems when used as priors. However, sampling from the resulting denoising pos-
terior distributions remains a challenge as it involves intractable terms. To tackle this issue,
state-of-the-art approaches formulate the problem as that of sampling from a surrogate dif-
fusion model targeting the posterior and decompose its scores into two terms: the prior score
and an intractable guidance term. While the former is replaced by the pre-trained score of
the considered diffusion model, the guidance term has to be estimated. In this paper, we
propose a novel approach that utilises a decomposition of the transitions which, in contrast
to previous methods, allows a trade-off between the complexity of the intractable guidance
term and that of the prior transitions. We validate the proposed approach through extensive
experiments on linear and nonlinear inverse problems, including challenging cases with latent
diffusion models as priors. We then demonstrate its applicability to various modalities and
its promising impact on public health by tackling cardiovascular disease diagnosis through
the reconstruction of incomplete electrocardiograms.
Website: Useful links. https://arxiv.org/abs/2410.09945, https://github.com/yazidjanati/mgps
In Room M7 101, 1st floor, Monod campus, ENSL.