相关论文: Measurement Embedded Schr\"odinger Bridge for Inve…

Consider the problem of matching two independent i.i.d. samples of size $N$ from two distributions $P$ and $Q$ in $\mathbb{R}^d$. For an arbitrary continuous cost function, the optimal assignment problem looks for the matching that…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

Recent advances in diffusion bridge models leverage Doob's $h$-transform to establish fixed endpoints between distributions, demonstrating promising results in image translation and restoration tasks. However, these approaches often produce…

The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…

Diffusion bridges (DBs) are a class of diffusion models that enable faster sampling by interpolating between two paired image distributions. Training traditional DBs for image reconstruction requires high-quality reference images, which…

Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants,…

We propose enforcing constraints on Model-Based Diffusion by introducing emerging barrier functions inspired by interior point methods. We demonstrate that the standard Model-Based Diffusion algorithm can lead to catastrophic performance…

Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize…

A Schr\"{o}dinger bridge establishes a dynamic transport map between two target distributions via a reference process, simultaneously solving an associated entropic optimal transport problem. We consider the setting where samples from the…

We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired samples drawn from arbitrary source and target distributions. Our method generalizes both 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 are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

Generating samples from a probability distribution is a fundamental task in machine learning and statistics. This article proposes a novel scheme for sampling from a distribution for which the probability density $\mu({\bf x})$ for ${\bf…

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such…

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger bridge matching, effectively learn mappings…

In recent advancements in proton therapy, MR-based treatment planning is gaining momentum to minimize additional radiation exposure compared to traditional CT-based methods. This transition highlights the critical need for accurate MR-to-CT…

This paper proposes a generative speech enhancement model based on Schr\"odinger bridge (SB). The proposed model is employing a tractable SB to formulate a data-to-data process between the clean speech distribution and the observed noisy…

We study a semimartingale optimal transport problem interpolating between the Schr\"odinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokhod embedding problem. The cost combines an entropy term on…

Diffusion bridge models offer a powerful framework for connecting two data distributions, such as in image restoration and translation. Many existing methods learn this bridge by mimicking the score-matching formulation of standard…

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…