Related papers: Multi-marginal temporal Schr\"odinger Bridge Match…
In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground…
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…
Markov state models (MSMs) are valuable for studying dynamics of protein conformational changes via statistical analysis of molecular dynamics (MD) simulations. In MSMs, the complex configuration space is coarse-grained into conformational…
Diffusion-based models have demonstrated remarkable effectiveness in image restoration tasks; however, their iterative denoising process, which starts from Gaussian noise, often leads to slow inference speeds. The Image-to-Image…
Diffusion models serve as a powerful generative framework for solving inverse problems. However, they still face two key challenges: 1) the distortion-perception tradeoff, where improving perceptual quality often degrades reconstruction…
Revealing the structure and dynamics of complex networked systems from observed data is of fundamental importance to science, engineering, and society. Is it possible to develop a universal, completely data driven framework to decipher the…
We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose…
We consider the discrete-time Schr\"odinger bridge problem on a finite state space. Although it has been known that the Iterative Markovian Fitting (IMF) algorithm converges in Kullback-Leibler divergence to the ground truth solution, the…
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…
Markov models of character substitution on phylogenies form the foundation of phylogenetic inference frameworks. Early models made the simplifying assumption that the substitution process is homogeneous over time and across sites in the…
Denoising diffusion bridge models (DDBMs) are a powerful variant of diffusion models for interpolating between two arbitrary paired distributions given as endpoints. Despite their promising performance in tasks like image translation, DDBMs…
Understanding the dynamics of a system is important in many scientific and engineering domains. This problem can be approached by learning state transition rules from observations using machine learning techniques. Such observed time-series…
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…
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,…
Multitemporal hyperspectral unmixing can capture dynamical evolution of materials. Despite its capability, current methods emphasize variability of endmembers while neglecting dynamics of abundances, which motivates our adoption of neural…
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…
We show that a pseudospectral representation of the wavefunction using multiple spatial domains of variable size yields a highly accurate, yet efficient method to solve the time-dependent Schr\"odinger equation. The overall spatial domain…
We analyze the Schr\"odingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schr\"odingerization technique, introduced in [31], transforms any linear ordinary and partial…
Diffusion in heterogeneous media partitioned by semi-permeable interfaces has a wide range of applications in the physical and life sciences, including gas permeation in soils, diffusion magnetic resonance imaging (dMRI), drug delivery,…
Hidden Markov Models (HMMs) comprise a powerful generative approach for modeling sequential data and time-series in general. However, the commonly employed assumption of the dependence of the current time frame to a single or multiple…