Related papers: Diffusion Schr\"odinger Bridge with Applications t…

Identifying the drift and diffusion of an SDE from its population dynamics is a notoriously challenging task. Researchers in machine learning and single-cell biology have only been able to prove a partial identifiability result: for…

The design of mean and variance schedules for the perturbed signal is a fundamental challenge in generative models. While score-based and Schr\"odinger bridge-based models require careful selection of the stochastic differential equation to…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the…

In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE) with a constant diffusion coefficient, and with time…

Entropy-regularized optimal transport, which has strong links to the Schr\"odinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed…

Score-based generative models (SGMs) have revolutionized the field of generative modeling, achieving unprecedented success in generating realistic and diverse content. Despite empirical advances, the theoretical basis for why optimizing the…

Score-based generative modeling (SBGM) has achieved state-of-the-art performance in image generation, with the quality of generated images being highly dependent on the design of the forward (diffusion) process. Among these, models based on…

Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by…

The mean-field Schr\"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline. Unlike the standard…

We propose Image-to-Image Schr\"odinger Bridge (I$^2$SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for…

Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…

We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…

We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint…

Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary…

Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…

This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods commonly employed in image and video applications. Unlike…

Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…

Diffusion models have emerged as powerful learned priors for solving inverse problems. However, current iterative solving approaches which alternate between diffusion sampling and data consistency steps typically require hundreds or…

Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…