相关论文: Simulating conditioned diffusions on manifolds

The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling…

Thermal multi-phase flow simulations are indispensable to understanding the multi-scale and multi-physics phenomena in metal additive manufacturing (AM) processes, yet accurate and robust predictions remain challenging. This book chapter…

It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous…

Recently, conditional diffusion models have gained popularity in numerous applications due to their exceptional generation ability. However, many existing methods are training-required. They need to train a time-dependent classifier or a…

Sparse distributions of seismic sensors and sources pose challenges for subsurface imaging, source characterization, and ground motion modeling. While large-N arrays have shown the potential of dense observational data, their deployment…

A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…

Distributed combustion, often associated with the low-oxygen condition, offers ultra-low NOX emission. However, it was recently achieved without combustion air dilution or internal flue gas recirculation, using a distinct approach called…

We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for…

The probability density is a fundamental quantity for characterizing diffusion processes. However, it is seldom known except in a few renowned cases, including Brownian motion and the Ornstein-Uhlenbeck process and their bridges, geometric…

We present a new method of deriving a boundary condition at a thin membrane for diffusion from experimental data. Based on experimental results obtained for normal diffusion of ethanol in water, we show that the derived boundary condition…

We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure…

Diffusion models achieve state-of-the-art performance in generating realistic objects and have been successfully applied to images, text, and videos. Recent work has shown that diffusion can also be defined on graphs, including graph…

Practically, training diffusion models typically requires explicit time conditioning to guide the network through the denoising sampling process. Especially in deterministic methods like DDIM, the absence of time conditioning leads to…

This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are build on our previously developed…

Bisimulation is a concept that captures behavioural equivalence of states in a variety of types of transition systems. It has been widely studied in discrete-time settings where a key notion is the bisimulation metric which quantifies "how…

We propose a new classification scheme for diffusion processes for which the backward Kolmogorov equation is solvable in analytically closed form by reduction to hypergeometric equations of the Gaussian or confluent type. The construction…

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

In this paper, a comprehensive examination of the temperature- and bias-dependent diffusion regimes of underdamped Brownian particles is presented. A temperature threshold for a transition between anomalous and normal diffusive behaviors is…

Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$, one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the…