Related papers: Exact simulation of the Wright-Fisher diffusion
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
We develop a general solution for the Fokker-Planck (Kolomogorov) equation representing the diffusion limit of the Wright-Fisher model of random genetic drift for an arbitrary number of alleles at a single locus. From this solution, we can…
We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…
Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…
Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the…
We explore the oscillatory behavior observed in inversion methods applied to large-scale text-to-image diffusion models, with a focus on the "Flux" model. By employing a fixed-point-inspired iterative approach to invert real-world images,…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
We show how to calculate individual terms of the Edgeworth series to approximate the distribution of the Pearson correlation coefficient with the help of a simple Mathematica program. We also demonstrate how to eliminate the corresponding…
Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also…
The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes. Here we have analyzed…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
We introduce a multi-allele Wright-Fisher model with non-recurrent, reversible mutation and directional selection. In this setting, the allele frequencies at a single locus track the path of a hybrid jump-diffusion process with state space…
Diffusion model deployment has been suffering from high energy consumption and inference latency despite its superior performance in visual generation tasks. Dynamic voltage and frequency scaling (DVFS) offers a promising solution to…
Neural network representations of simple models, such as linear regression, are being studied increasingly to better understand the underlying principles of deep learning algorithms. However, neural representations of distributional…
The present research proposes a new memory-efficient method using diffusion models to inject turbulent inflow conditions into Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for various flow problems. A guided diffusion…
Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical…
Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination…
Class-labeled datasets, particularly those common in scientific domains, are rife with internal structure, yet current class-conditional diffusion models ignore these relationships and implicitly diffuse on all classes in a flat fashion. To…
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…