Related papers: A Closed-Form Framework for Schr\"odinger Bridges …
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…
Erwin Schroedinger posed, and to a large extent solved in 1931/32 the problem of finding the most likely random evolution between two continuous probability distributions. This article considers this problem in the case when only samples of…
Stochastic unravelings allow to efficiently simulate open system dynamics, yet their application has traditionally been restricted to master equations that preserve both Hermiticity and trace. In this work, we introduce a general framework…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
We introduce Triangular-Reference Schr\"odinger Bridges for Time Series (TR-SBTS), a conservative extension of the SBTS framework in which the Brownian reference is replaced by an intervalwise frozen, possibly degenerate diffusion…
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…
The unbalanced Schr\"odinger bridge problem (uSBP) seeks to interpolate between a probability measure $\rho_0$ and a sub-probability measure $\rho_T$ while minimizing KL divergence to a reference measure $\mathbf{R}$ on a path space. In…
In 1931/32, Schroedinger studied a hot gas Gedankenexperiment, an instance of large deviations of the empirical distribution and an early example of the so-called maximum entropy inference method. This so-called Schroedinger bridge problem…
Density ratio estimation is fundamental to tasks involving $f$-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports -- the density-chasm and the support-chasm…
Recent advancements in optimization-based text-to-3D generation heavily rely on distilling knowledge from pre-trained text-to-image diffusion models using techniques like Score Distillation Sampling (SDS), which often introduce artifacts…
A Schr\"odinger bridge is the most probable time-dependent probability distribution that connects an initial probability distribution $w_{i}$ to a final one $w_{f}$. The problem has been solved and widely used for the case of simple…
A computational PDE-constrained optimization approach is proposed for optimal trajectory planning under uncertainty by means of an associated Schroedinger Bridge Problem (SBP). The proposed SBP formulation is interpreted as the mean-field…
We propose to learn a generative model via entropy interpolation with a Schr\"{o}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the…
Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…
Motivated by modern machine learning applications where we only have access to empirical measures constructed from finite samples, we relax the marginal constraints of the classical Schr\"odinger bridge problem by penalizing the transport…
We introduce a distribution-free lattice Boltzmann formulation for general compartmental reaction--diffusion systems arising in mathematical epidemiology. The proposed scheme, termed a single-step simplified lattice Boltzmann method…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
We study the Schr\"{o}dinger bridge problem (SBP) with nonlinear prior dynamics. In control-theoretic language, this is a problem of minimum effort steering of a given joint state probability density function (PDF) to another over a finite…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…