Related papers: Score-based deterministic density sampling
We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of…
Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their inference is very slow due to a need for many (e.g., 2000) iterations of sequential…
We present a framework that allows for the non-asymptotic study of the $2$-Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation and the distribution of its numerical approximation in the…
Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on ${\mathbb R}^d$. In this setting, the objective is in general not…
There has been recently a lot of interest in the analysis of the Stein gradient descent method, a deterministic sampling algorithm. It is based on a particle system moving along the gradient flow of the Kullback-Leibler divergence towards…
Discrete diffusion models have emerged as a powerful paradigm for generative modeling on sequence data; however, the information-theoretic principles governing their reverse processes remain significantly less understood than those of their…
Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper develops a theoretical framework for understanding the…
Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…
We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…
Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…
We study variance reduction for score estimation and diffusion-based sampling in settings where the clean (target) score is available or can be approximated. Starting from the Target Score Identity (TSI), which expresses the noisy marginal…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a…
Drifting models train one-step generators by optimizing a kernel-induced mean-shift discrepancy between the data and model distributions, with Laplace kernels used by default in practice. At each point, this discrepancy compares the…
We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E…
Current discriminative depth estimation methods often produce blurry artifacts, while generative approaches suffer from slow sampling due to curvatures in the noise-to-depth transport. Our method addresses these challenges by framing depth…
Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…