Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:00 pm
Date: 26th January
Place: 3001

Eric MOULINES (EPITA & MBZUAI) – Sampling Posteriors with Implicit Priors: Diffusion Models, Guidance Bias, and SMC

 Abstract: 

We study Bayesian sampling for inverse problems where the goal is to reconstruct a signal $X$ from noisy observations $Y=A(X)+\sigma Z$ while providing uncertainty quantification. The posterior can be written as $\pi(dx)\propto g(x)\rho(dx)$, where $g$ is a potential (typically the likelihood) and $\rho$ is an implicit prior approximated by a diffusion model (DDPM). This setting makes standard approaches that rely on evaluating the prior density intractable. We review guidance methods that modify the denoising dynamics using score-based terms (notably via Tweedie’s formula), and we highlight the biases introduced by approximating intermediate potentials. We then present a “sequence of distributions” viewpoint: the exact posterior path is replaced by a chain of distributions bridging a reference Gaussian to the target, described through a Feynman–Kac representation and simulable with SMC/particle methods. Finally, we discuss Monte Carlo guidance schemes and mixture-based approaches, including a data-augmentation formulation and a deterministic Gibbs sampler, and we illustrate these ideas on imaging tasks (super-resolution, deblurring, inpainting) and audio source separation.

Organizers:

Anna KORBA (CREST), Vincent DIVOL (CREST), Jaouad MOURTADA (CREST)

Sponsors:
CREST-CMAP