Related papers: A Mixture-Based Framework for Guiding Diffusion Mo…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…
Many inverse problems are ill-posed and need to be complemented by prior information that restricts the class of admissible models. Bayesian approaches encode this information as prior distributions that impose generic properties on the…
The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires…
Diffusion models optimized via variational inference (VI) have emerged as a promising tool for generating samples from unnormalized target densities. These models create samples by simulating a stochastic differential equation, starting…
This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
Many inverse problems arising in applications come from continuum models where the unknown parameter is a field. In practice the unknown field is discretized resulting in a problem in $\mathbb{R}^N$, with an understanding that refining the…
The choice of prior is central to solving ill-posed imaging inverse problems, making it essential to select one consistent with the measurements $y$ to avoid severe bias. In Bayesian inverse problems, this could be achieved by evaluating…
Score-based diffusion models have recently been extended to infinite-dimensional function spaces, with uses such as inverse problems arising from partial differential equations. In the Bayesian formulation of inverse problems, the aim is to…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…
In this paper, we present a novel approach to fitting mixture models based on estimating first the posterior distribution of the auxiliary variables that assign each observation to a group in the mixture. The posterior distributions of the…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…
Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on…
Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not…
Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However,…
Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly…
Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…
The recent emergence of diffusion models has significantly advanced the precision of learnable priors, presenting innovative avenues for addressing inverse problems. Since inverse problems inherently entail maximum a posteriori estimation,…
We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…