Related papers: Reflected Schr\"odinger Bridge for Constrained Gen…

Generative diffusion models use time-forward and backward stochastic differential equations to connect the data and prior distributions. While conventional diffusion models (e.g., score-based models) only learn the backward process, more…

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,…

We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…

While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…

Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area: one based on discriminative models and one based on generative…

Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Mass transport problems arise in many areas of machine learning whereby one wants to compute a map transporting one distribution to another. Generative modeling techniques like Generative Adversarial Networks (GANs) and Denoising Diffusion…

The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schr\"odinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent…

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…

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…

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,…

Compared to the existing function-based models in deep generative modeling, the recently proposed diffusion models have achieved outstanding performance with a stochastic-process-based approach. But a long sampling time is required for this…

Metasurface inverse design is challenged by the intricate relationship between structural parameters and electromagnetic responses, as well as the high dimensionality of the optimization space. Local models, while commonly employed, quickly…

Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution…

Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more…

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…

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…

We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of…

Schr\"odinger bridge (SB) has emerged as the go-to method for optimizing transportation plans in diffusion models. However, SB requires estimating the intractable forward score functions, inevitably resulting in the costly implicit training…