Related papers: Go With the Flow: Fast Diffusion for Gaussian Mixt…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
Recent advancements in diffusion bridges for distribution transport problems have heavily relied on matching frameworks, yet existing methods often face a trade-off between scalability and access to optimal pairings during training. Fully…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to…
In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or…
Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic…
We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem…
Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual…
Consider a reference Markov process with initial distribution $\pi_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $\pi_{T}$, which is not equal to the marginal…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
Stochastic flows of an advective-diffusive nature are ubiquitous in physical sciences. Of particular interest is the problem to reconcile observed marginal distributions with a given prior posed by E. Schrodinger in 1932/32 and known as the…
The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and the reciprocal class, successfully solves the Schr\"odinger Bridge (SB) problem. However, an efficient practical…
Diffusion bridges (DBs) are a class of diffusion models that enable faster sampling by interpolating between two paired image distributions. Training traditional DBs for image reconstruction requires high-quality reference images, which…
Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable…
Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce…
A Schr\"{o}dinger bridge establishes a dynamic transport map between two target distributions via a reference process, simultaneously solving an associated entropic optimal transport problem. We consider the setting where samples from the…
In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schr\"odinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular…
Score-based diffusion models are frequently employed as structural priors in inverse problems. However, their iterative denoising process, initiated from Gaussian noise, often results in slow inference speeds. The Image-to-Image…
Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal…