Related papers: Split Gibbs Discrete Diffusion Posterior Sampling
We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in…
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…
Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while…
Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical…
We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…
Solving inverse problems with the reverse process of a diffusion model represents an appealing avenue to produce highly realistic, yet diverse solutions from incomplete and possibly noisy measurements, ultimately enabling uncertainty…
In signal processing, the data collected from sensing devices is often a noisy linear superposition of multiple components, and the estimation of components of interest constitutes a crucial pre-processing step. In this work, we develop a…
Recent diffusion distillation methods have achieved remarkable progress, enabling high-quality ${\sim}4$-step sampling for large-scale text-conditional image and video diffusion models. However, further reducing the number of sampling steps…
In a great number of tasks in science and engineering, the goal is to infer an unknown image from a small number of measurements collected from a known forward model describing certain sensing or imaging modality. Due to resource…
Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…
Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling…
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…
Restoring degraded music signals is essential to enhance audio quality for downstream music manipulation. Recent diffusion-based music restoration methods have demonstrated impressive performance, and among them, diffusion posterior…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
We present a performant, general-purpose gradient-guided nested sampling algorithm, ${\tt GGNS}$, combining the state of the art in differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested…
Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has…
Score Distillation Sampling (SDS) has been pivotal for leveraging pre-trained diffusion models in downstream tasks such as inverse problems, but it faces two major challenges: $(i)$ mode collapse and $(ii)$ latent space inversion, which…
Diffusion models have emerged as an expressive family of generative models rivaling GANs in sample quality and autoregressive models in likelihood scores. Standard diffusion models typically require hundreds of forward passes through the…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…