Related papers: Riemannian Diffusion Schr\"odinger Bridge
Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured,…
Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms…
We study Diffusion Schr\"odinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the…
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling…
We introduce a score-based generative sampling method for solving the nonlinear filtering problem with robust accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low stability. To overcome this…
Modality translation is inherently under-constrained, as multiple cross-modal mappings may yield the same marginals. Recent work has shown that diffusion bridges are effective for this task. However, most existing approaches rely on fully…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
Controllable image generation is fundamental to the success of modern generative AI, yet it faces a critical trade-off between semantic fidelity and inference speed. The RemEdit diffusion-based framework addresses this trade-off with two…
Graph structures offer a versatile framework for representing diverse patterns in nature and complex systems, applicable across domains like molecular chemistry, social networks, and transportation systems. While diffusion models have…
Diffusion models are powerful deep generative models, but unlike classical models, they lack an explicit low-dimensional latent space that parameterizes the data manifold. This absence makes it difficult to perform manifold-aware…
Euclidean diffusion models have achieved remarkable success in generative modeling across diverse domains, and they have been extended to manifold cases in recent advances. Instead of explicitly utilizing the structure of special manifolds…
We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…
A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic…
In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular, we introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form…
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…
Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main…
This paper explores the use of score-based diffusion models for Bayesian image reconstruction. Diffusion models are an efficient tool for generative modeling. Diffusion models can also be used for solving image reconstruction problems. We…
Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on…
Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability…
Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling. In this work we conduct a systematic comparison and theoretical analysis of different approaches to learning conditional…