Related papers: Learning non-equilibrium diffusions with Schr\"odi…
This work studies the Schr\"odinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial and terminal densities supported over the Lie group while…
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…
Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal…
We propose an extension of the Schr\"odinger equation for a quantum system interacting with environment. This equation describes dynamics of auxiliary wave-functions $\mathbf{m}$, from which the system density matrix can be reconstructed as…
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…
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…
Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in…
The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…
Diffusion and Schr\"{o}dinger Bridge models have established state-of-the-art performance in generative modeling but are often hampered by significant computational costs and complex training procedures. While continuous-time bridges…
Schr\"odinger Bridges (SB) have recently gained the attention of the ML community as a promising extension of classic diffusion models which is also interconnected to the Entropic Optimal Transport (EOT). Recent solvers for SB exploit the…
We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian…
Resampling from a target measure whose density is unknown is a fundamental problem in mathematical statistics and machine learning. A setting that dominates the machine learning literature consists of learning a map from an easy-to-sample…
The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
In this work, we study a discrete Schr\"odinger bridge problem with partial marginal observations. A main difficulty compared to the classical Schr\"odinger bridge formulation is that our problem is not strictly convex and standard…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…
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 provide the exact analytic solution of the stochastic Schr\"odinger equation describing an harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of…
Schr\"{o}dinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schr\"{o}dinger bridge…
Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…