Related papers: Simulating bridges using confluent diffusions
The accurate and robust simulation of transcritical real-fluid flows is crucial for many engineering applications. Diffused interface methods are frequently employed and several numerical schemes have been developed for simulating…
We study a sequential Monte Carlo algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. We use the practical and popular geometric annealing schedule, and use a Langevin diffusion at each…
Due to network operation and maintenance relying heavily on network traffic monitoring, traffic matrix analysis has been one of the most crucial issues for network management related tasks. However, it is challenging to reliably obtain the…
In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common…
Schrodinger Bridges (SBs) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been…
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
Diffusion bridges have shown potential in paired image-to-image (I2I) translation tasks. However, existing methods are limited by their unidirectional nature, requiring separate models for forward and reverse translations. This not only…
Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…
Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these approximations asymptotically, they do not quantify the error…
We propose a highly efficient and accurate methodology for generating synthetic financial market data using a diffusion model approach. The synthetic data produced by our methodology align closely with observed market data in several key…
We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…
Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions are considered. Under these conditions, a concentration of…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
The randomized midpoint method, proposed by [SL19], has emerged as an optimal discretization procedure for simulating the continuous time Langevin diffusions. Focusing on the case of strong-convex and smooth potentials, in this paper, we…
Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge…
Many modern biological assays, including RNA sequencing, yield integer-valued counts that reflect the number of molecules detected. These measurements are often not at the desired resolution: while the unit of interest is typically a single…
Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…
Generative diffusion models are extensively used in unsupervised and self-supervised machine learning with the aim to generate new samples from a probability distribution estimated with a set of known samples. They have demonstrated…